Researcher basic information

• 博士（数理科学）, The University of Tokyo, Mar. 2001

• https://researchmap.jp/CCSD22aP?lang=en

• https://jglobal.jst.go.jp/detail?JGLOBAL_ID=202001019806009457

• 90346065

• 202001019806009457

• Natural Science, Algebra, arithmetic geometry
• Natural Science, Algebra, number theory

• Bachelor's degree program, School of Science
• Master's degree program, Graduate School of Science
• Doctoral (PhD) degree program, Graduate School of Science

Research activity information

• Semistable representations as limits of crystalline representations
  Anand Chitrao; Eknath Ghate; Seidai Yasuda
  Algebra & Number Theory, 19, 6, 1049, 1097, Mathematical Sciences Publishers, 14 May 2025, [Peer-reviewed]
  Scientific journal
• Kato's epsilon conjecture for anticyclotomic CM deformations at inert primes
  Ashay A. Burungale; Shinichi Kobayashi; Kazuto Ota; Seidai Yasuda
  Journal of Number Theory, 270, 17, 67, Elsevier BV, May 2025, [Peer-reviewed]
  Scientific journal
• Theory of heat equations for sigma functions
  J. Chris Eilbeck; John Gibbons; Yoshihiro Ônishi; Seidai Yasuda
  Glasgow Mathematical Journal, 1, 58, Cambridge University Press (CUP), 28 Feb. 2025, [Peer-reviewed]
  Scientific journal, Abstract
  
  Let $e$ and $q$ be fixed co-prime integers satisfying $1\lt e\lt q$ . Let $\mathscr {C}$ be a certain family of deformations of the curve $y^e=x^q$ . That family is called the $(e,q)$ -curve and is one of the types of curves called plane telescopic curves. Let $\varDelta$ be the discriminant of $\mathscr {C}$ . Following pioneering work by Buchstaber and Leykin (BL), we determine the canonical basis $\{ L_j \}$ of the space of derivations tangent to the variety $\varDelta =0$ and describe their specific properties. Such a set $\{ L_j \}$ gives rise to a system of linear partial differential equations (heat equations) satisfied by the function $\sigma (u)$ associated with $\mathscr {C}$ , and eventually gives its explicit power series expansion. This is a natural generalisation of Weierstrass’ result on his sigma function. We attempt to give an accessible description of various aspects of the BL theory. Especially, the text contains detailed proofs for several useful formulae and known facts since we know of no works which include their proofs.
• Arithmetic Quotients of the Bruhat-Tits Building for Projective General Linear Group in Positive Characteristic
  Satoshi Kondo; Seidai Yasuda
  Memoirs of the American Mathematical Society, 306, 1547, American Mathematical Society (AMS), 27 Jan. 2025, [Peer-reviewed]
  Scientific journal,

  Let . We study a subspace of the space of automorphic forms of over a global field of positive characteristic (or, a function field of a curve over a finite field). We fix a place of , and we consider the subspace consisting of automorphic forms such that the local component at of the associated automorphic representation is the Steinberg representation (to be made precise in the text).

  We have two results.

  One theorem (Theorem 5.4.2) describes the constituents of as automorphic representation and gives a multiplicity one type statement.

  For the other theorem (Theorem 4.5.1), we construct, using the geometry of the Bruhat-Tits building, an analogue of modular symbols in integrally (that is, in the space of -valued automorphic forms). We show that the quotient is finite when a level is fixed and give a bound on the exponent of this quotient.

• Local newforms for generic representations of unramified odd unitary groups and the Fundamental Lemma
  Hiraku Atobe; Masao Oi; Seidai Yasuda
  Duke Mathematical Journal, 173, 12, Duke University Press, 01 Sep. 2024, [Peer-reviewed]
  Scientific journal
• Local newforms for the general linear groups over a non-archimedean local field
  Hiraku Atobe; Satoshi Kondo; Seidai Yasuda
  Forum of Mathematics, Pi, 10, Cambridge University Press (CUP), 2022, [Peer-reviewed]
  Scientific journal, Abstract
  
  In [14], Jacquet–Piatetskii-Shapiro–Shalika defined a family of compact open subgroups of p-adic general linear groups indexed by nonnegative integers and established the theory of local newforms for irreducible generic representations. In this paper, we extend their results to all irreducible representations. To do this, we define a new family of compact open subgroups indexed by certain tuples of nonnegative integers. For the proof, we introduce the Rankin–Selberg integrals for Speh representations.
• Regularity of quotients of Drinfeld modular schemes
  Satoshi Kondo; Seidai Yasuda
  Pacific Journal of Mathematics, 304, 2, 481, 503, Mathematical Sciences Publishers, 12 Feb. 2020, [Peer-reviewed]
  Scientific journal, Let A be the coordinate ring of a projective smooth curve over a finite field minus a closed point. For a nontrivial ideal I⊂A, Drinfeld defined the notion of structure of level I on a Drinfeld module.
  
  We extend this to that of level N, where N is a finitely generated torsion A-module. The case where N=(I−1/A)d, where d is the rank of the Drinfeld module, coincides with the structure of level I. The moduli functor is representable by a regular affine scheme.
  
  The automorphism group AutA(N) acts on the moduli space. Our theorem gives a class of subgroups for which the quotient of the moduli scheme is regular. Examples include generalizations of Γ0 and of Γ1. We also show that parabolic subgroups appearing in the definition of Hecke correspondences are such subgroups.
• Belyi’s theorem in characteristic two
  Yusuke Sugiyama; Seidai Yasuda
  Compositio Mathematica, 156, 2, 325, 339, Wiley, Feb. 2020, [Peer-reviewed], [International Magazine]
  Scientific journal, We prove an analogue of Belyi’s theorem in characteristic two. Our proof consists of the following three steps. We first introduce a new notion called pseudo-tameness for morphisms between curves over an algebraically closed field of characteristic two. Secondly, we prove the existence of a ‘pseudo-tame’ rational function by showing the vanishing of an obstruction class. Finally, we construct a tamely ramified rational function from the ‘pseudo-tame’ rational function.
• Category of mixed plectic Hodge structures
  Kenichi Bannai; Kei Hagihara; Shinichi Kobayashi; Kazuki Yamada; Shuji Yamamoto; Seidai Yasuda
  Asian Journal of Mathematics, 24, 1, 31, 76, International Press of Boston, 2020, [Peer-reviewed]
  Scientific journal
• First and second K-groups of an elliptic curve over a global field of positive characteristic
  Satoshi Kondo; Seidai Yasuda
  Annales de l’institut Fourier, 68, 5, 2005, 2067, Nov. 2018, [Peer-reviewed], [International Magazine]
  Scientific journal
• Sites whose topoi are the smooth representations of locally prodiscrete monoids
  Satoshi Kondo; Seidai Yasuda
  Journal of Algebra, 502, 382, 496, May 2018, [Peer-reviewed], [International Magazine]
  Scientific journal
• The radius of convergence of the p-adic sigma function
  Kenichi Bannai; Shinichi Kobayashi; Seidai Yasuda
  Mathematische Zeitschrift, 286, 1-2, 751, 781, Jun. 2017, [Peer-reviewed]
  Scientific journal
• Finite real multiple zeta values generate the whole space Z
  Seidai Yasuda
  INTERNATIONAL JOURNAL OF NUMBER THEORY, 12, 3, 787, 812, May 2016, [Peer-reviewed], [International Magazine]
  English, Scientific journal
• On some applications of integral p-adic Hodge theory to Galois representations
  Go Yamashita; Seidai Yasuda
  JOURNAL OF NUMBER THEORY, 147, 721, 748, Feb. 2015, [Peer-reviewed], [International Magazine]
  English, Scientific journal
• On two higher Chow groups of schemes over a finite field
  Satoshi Kondo; Seidai Yasuda
  DOCUMENTA MATHEMATICA, 20, 737, 752, 2015, [Peer-reviewed], [International Magazine]
  English, Scientific journal
• The Hoffman basis of the space of multiple zeta values
  Yasuda Seidai
  RIMS Kokyuroku Bessatsu, 51, 51, 375, 433, 京都大学, Oct. 2014, [Peer-reviewed]
  Japanese, Recently Brown [Br1] gave a proof of a conjecture by Hoffman [Hof2] that the Q-vector space generated by the multiple zeta values is generated by the set, called the Hoffman basis, of multiple zeta values of a certain special type. In this article we give a survey of this topic including an outline of the proof by Brown [Br1]. At the end of the article we also give some applications of the result and mention some open problems.
• The Riemann-Roch theorem without denominators in motivic homotopy theory
  Satoshi Kondo; Seidai Yasuda
  JOURNAL OF PURE AND APPLIED ALGEBRA, 218, 8, 1478, 1495, Aug. 2014, [Peer-reviewed], [International Magazine]
  English, Scientific journal
• The l-parity conjecture for abelian varieties over function fields of characteristic p>0
  Fabien Trihan; Seidai Yasuda
  COMPOSITIO MATHEMATICA, 150, 4, 507, 522, Apr. 2014, [Peer-reviewed], [International Magazine]
  English, Scientific journal
• Explicit t-expansions for the elliptic curve y^2=4(x^3 + Ax + B)
  Seidai Yasuda
  PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 89, 9, 123, 127, Nov. 2013, [Peer-reviewed]
  English, Scientific journal
• Zeta elements in the K-theory of Drinfeld modular varieties
  Satoshi Kondo; Seidai Yasuda
  MATHEMATISCHE ANNALEN, 354, 2, 529, 587, Oct. 2012, [Peer-reviewed], [International Magazine]
  English, Scientific journal
• Local L and epsilon factors in Hecke eigenvalues
  Satoshi Kondo; Seidai Yasuda
  JOURNAL OF NUMBER THEORY, 132, 9, 1910, 1948, Sep. 2012, [Peer-reviewed]
  English, Scientific journal
• On the second rational K-group of an elliptic curve over global fields of positive characteristic
  Satoshi Kondo; Seidai Yasuda
  PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 102, 1053, 1098, Jun. 2011, [Peer-reviewed], [International Magazine]
  English, Scientific journal
• Product structures in motivic cohomology and higher Chow groups
  Satoshi Kondo; Seidai Yasuda
  JOURNAL OF PURE AND APPLIED ALGEBRA, 215, 4, 511, 522, Apr. 2011, [Peer-reviewed], [International Magazine]
  English, Scientific journal
• Non-negativity of the Fourier coefficients of eta products associated to regular systems of weights
  Seidai Yasuda
  PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 46, 3, 549, 563, Sep. 2010, [Peer-reviewed]
  English, Scientific journal
• Haramonic and equianharmonic equaitons in the Grothendieck-Teuchmuller group. III
  Hiroaki Nakamura; Hiroshi Tsunogai; Seidai Yasuda
  JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, 9, 2, 431, 448, Apr. 2010, [Peer-reviewed], [International Magazine]
  English, Scientific journal
• On Haagerup's list of potential principal graphs of subfactors
  Marta Asaeda; Seidai Yasuda
  COMMUNICATIONS IN MATHEMATICAL PHYSICS, 286, 3, 1141, 1157, Mar. 2009, [Peer-reviewed], [International Magazine]
  English, Scientific journal
• The product formula for local constants in torsion rings
  Seidai Yasuda
  JOURNAL OF MATHEMATICAL SCIENCES-THE UNIVERSITY OF TOKYO, 16, 2, 199, 230, 2009, [Peer-reviewed]
  English, Scientific journal
• Local constants in torsion rings
  Seidai Yasuda
  JOURNAL OF MATHEMATICAL SCIENCES-THE UNIVERSITY OF TOKYO, 16, 2, 125, 197, 2009, [Peer-reviewed]
  English, Scientific journal
• Laurent Lafforgue 氏の業績 : 関数体上のGL_rに対する Langlands 対応の確立
  安田 正大
  数学, 60, 4, 415, 424, 日本数学会, Oct. 2008
  Japanese, 2002年の国際数学者会議において Fields 賞を受賞した，Laurent Lafforgue 氏の業績を紹介することが本稿の目的である.
• Local ε0-characters in torsion rings
  Seidai Yasuda
  Journal de Theorie des Nombres de Bordeaux, 19, 3, 763, 797, Universite de Bordeaux I, 2007, [Peer-reviewed]
  English, Scientific journal
• K-THEORETIC ELEMENTS ON DRINFELD MODULAR VARIETIES AND SPECIAL L-VALUES(Algebraic Number Theory and Related Topics)
  KONDO SATOSHI; YASUDA SEIDAI
  RIMS Kokyuroku, 1521, 1521, 66, 69, 京都大学数理解析研究所, Oct. 2006
  Japanese
• 志村曲線のCMサイクルとSafarevich-Tate群 (代数的整数論とその周辺)
  安田 正大
  数理解析研究所講究録, 1097, 1097, 139, 143, 京都大学数理解析研究所, Apr. 1999
  Japanese

• The Borel-Moore homology of an arithmetic quotient of the Bruhat-Tits building of PGL of a non-archimedean local field in positive characteristic and modular symbols
  Satoshi Kondo; Seidai Yasuda, 27 Jun. 2014
  We study the homology and the Borel-Moore homology with coefficients in
  
  $\mathbb{Q}$ of a quotient (called arithmetic quotient) of the Bruhat-Tits
  
  building of $\mathrm{PGL}$ of a nonarchimedean local field of positive
  
  characteristic by an arithmetic subgroup (a special case of the general
  
  definition in Harder's article (Invent.\ Math.\ 42, 135-175 (1977)).
  
  We define an analogue of modular symbols in this context and show that the
  
  image of the canonical map from homology to Borel-Moore homology is contained
  
  in the sub $\mathbb{Q}$-vector space generated by the modular symbols.
  
  By definition, the limit of the Borel-Moore homology as the arithmetic group
  
  becomes small is isomorphic to the space of $\mathbb{Q}$-valued automorphic
  
  forms that satisfy certain conditions at a distinguished (fixed) place (namely
  
  that it is fixed by the Iwahori subgroup and the center at the place). We show
  
  that the limit of the homology with $\mathbb{C}$-coefficients is identified
  
  with the subspace consisting of cusp forms. We also describe an irreducible
  
  subquotient of the limit of Borel-Moore homology as an induced representation
  
  in a precise manner and give a multiplicity one type result., Technical report
• Hoffman予想について (特集 ｢想定外｣の数学)
  安田 正大, 数学セミナー, 51, 1, 8, 12, Jan. 2012
  日本評論社, Japanese

• Additions and M-operations
  Seidai Yasuda
  Low dimensional topology and number theory XV, Mar. 2025
  [Invited]
• Some approaches for understanding symmetries of the multiple zeta values
  Seidai Yasuda
  17th MSJ-SI Lectures of multiple zeta values and beyond, Feb. 2025
  [Invited]
• On fine structures of two-dimensional crystalline representations
  Seidai Yasuda
  Workshop on Shimura varieties, representation theory and related topics, 2024, Oct. 2024
  [Invited]
• On the construction of some Wach modules of rank two and some integral structures of two-dimensional crystalline representations
  Seidai Yasuda
  Number theory seminar in Lille, 26 Sep. 2024
  [Invited]
• Geometry related with the absolute Galois group of Q_p
  Seidai Yasuda
  Workshop Arithmetic and Homotopic Geometry 2023, Mar. 2023
  [Invited]
• Local newforms and local L-factors for the general linear groups
  Seidai Yasuda
  10-th East Asia Number Theory Conference, Jan. 2023
  [Invited]
• Local newforms for the general linear groups from topos theoretic viewpoint
  Seidai Yasuda
  9th Kyoto conference on automorphic forms, Jun. 2022
  [Invited]
• Local newforms for the general linear groups
  Seidai Yasuda
  Automorphic form, automorphic L-functions and related topics, 25 Jan. 2022, English
  24 Jan. 2022 - 28 Jan. 2022, 36978292, [Invited]
• Vincent Lafforgue による関数体の Langlands 対応の構成
  安田 正大
  代数的整数論とその周辺, 11 Dec. 2019, English
  [Invited], [Domestic Conference]
• Integral structures of two dimensional crystalline representations
  Seidai Yasuda
  p-adic methods in arithmetic geometry at Sendai, 2019, 11 Nov. 2019, English
  [Invited], [International presentation]
• Cotangent complex and Postnikov towers
  Seidai Yasuda
  Yatsugatake Workshop, 2019, 02 Sep. 2019, English
  [Invited], [International presentation]
• Depth graded structures
  Seidai Yasuda
  Multiple zeta values and related topics, 12 Jun. 2019, English
  [Invited], [International presentation]
• 重さ (p^2+1)/2 以下の 2 次元クリスタリン表現の整構造.
  安田 正大
  早稲田大学整数論セミナー, 26 Apr. 2019, Japanese
  [Invited], [Domestic Conference]
• Modular complexes and dimensions of derived double shuffle modules
  Seidai Yasuda
  第17回北陸数論研究集会, 27 Dec. 2018, English
  [Invited], [Domestic Conference]
• A product of Eisenstein series and special L-values over the rational function field
  Seidai Yasuda
  NTCS Seminar on Number Theory, 21 Dec. 2018, English
  [Invited], [International presentation]
• Derived double shuffle Lie algebra and the Steinberg modules
  Seidai Yasuda
  NTCS Seminar on Number Theory, 19 Dec. 2018, English
  [Invited], [International presentation]
• Foliations I, II
  Seidai Yasuda
  八ヶ岳ワークショップ, 2018 The conservative conjecture, 20 Sep. 2018, English
  [Invited], [International presentation]
• 「p進多重ゼータ値」から「有限多重ゼータ値」へ
  安田 正大
  第２６回整数論サマースクール「多重ゼータ値」, 11 Sep. 2018, Japanese
  [Invited], [Domestic Conference]
• 結合子と結合子関係式
  安田 正大
  第２６回整数論サマースクール勉強会「モチヴィック多重ゼータ値」, 04 Aug. 2017, Japanese
  [Invited], [Domestic Conference]
• Drinfeld modular 多様体上の zeta 元について
  安田 正大
  九大数理談話会, 22 Jun. 2017, Japanese
  [Invited], [Domestic Conference]
• Linearized and derived double shuffle Lie algebras
  Seidai Yasuda
  Workshop: Johnson homomorphisms and related topics, 24 May 2017, English
  [Invited], [International presentation]
• pseudo-tame rational functions on curves in characteristic two
  Seidai Yasuda
  Weekly Seminar of the Laboratory of Algebraic Geometry and its Applications, 21 Mar. 2017, English
  [Invited], [International presentation]
• Ihara bracket for gorup schemes
  Seidai Yasuda
  Low dimensional topology and number theory IX, 16 Mar. 2017, English
  [Invited], [Domestic Conference]
• Belyi's theorem in charcteristic two
  Seidai Yasuda
  p-adic methods in arithmetic geometry at Sendai, 2016, 31 Oct. 2016, English
  [Invited], [International presentation]
• Etale theta functions, mono-theta enviroments, and [IUTeichI] \S1-\S3, I, II
  Seidai Yasuda
  Inter-iniversal Teichmuller Theory Summit 2016, 19 Jul. 2016, English
  [Invited], [International presentation]
• Topic on multiple zeta values
  Seidai Yasuda
  NCTS Number Theory Seminar, 22 Dec. 2015, English
  [Invited], [International presentation]
• モチフィック多重ゼータ値と有限多重ゼータ値
  安田 正大
  日本数学会２０１５年度秋季総合分科会, 16 Sep. 2015, Japanese
  [Invited], [Domestic Conference]
• Motivic and finite multiple zeta values
  Seidai Yasuda
  Bousfield localizations form a set: a workshop in memory of Tetsusuke Ohkawa, 30 Aug. 2015, English
  [Invited], [International presentation]
• 階数２のWach加群の族の構成
  安田 正大
  九大代数学セミナー, 12 Jun. 2015, Japanese
  [Invited], [Domestic Conference]
• Grids and the associated monoids
  Seidai Yasuda
  上智大学数学談話会, 22 May 2015, Japanese
  [Invited], [Domestic Conference]
• Integrality of p-adic multiple zeta values and application to finite multiple zeta values
  Seidai Yasuda
  東京北京パリ数論幾何セミナー, 08 Apr. 2015, English
  [Invited], [International presentation]
• Outlines: Kisin's proof of Breuil-Mezard conjecture
  Seidai Yasuda
  Winter school of p-adic Hodge theory, 16 Jan. 2015, English
  [Invited], [International presentation]
• Integrality and a conjectural relation between $p$-adic multizeta values and truncated multiple harmonic sums
  Seidai Yasuda
  Novel visage of arithmetic and derived geometry, 10 Oct. 2014, English
  [Invited], [Domestic Conference]
• p-adic multiple zeta values and truncated multiple harmonic sums
  Seidai Yasuda
  Workshop on Multiple Zeta Values, 22 Aug. 2014, English
  [Invited], [International presentation]
• eriods of Mixed Tate Motives and Multiple Zeta Values
  Seidai Yasuda
  2014 NCTS Lecture Series on Number Theory, 02 May 2014, English
  [Invited], [International presentation]
• 有限実多重ゼータ値と $p$ 進多重ゼータ値
  安田 正大
  第 20 回関西多重ゼータ研究会＆第 7 回多重ゼータ研究集会, 23 Feb. 2014, Japanese
  [Invited], [Domestic Conference]
• GL_d の smooth 表現の Galois 圏論的解釈と保型 Euler 系
  安田 正大
  九州代数的整数論 2013, 13 Feb. 2013, Japanese
  [Invited], [Domestic Conference]
• 多重ゼータ値についての最近の進展とドゥリーニュ・伊原予想
  安田 正大
  代数的整数論とその周辺, 04 Dec. 2012, Japanese
  [Invited], [Domestic Conference]
• Galois represetations attached to Siegel modular forms I、ＩＩ
  Seidai Yasuda
  The 15th Hakuba Autumn Workshop on Number Theory, 01 Nov. 2012, English
  [Invited], [International presentation]
• p-adic representations and p-adic Hodge theory
  Seidai Yasuda
  L-functions and Arithmetic, 22 Oct. 2012, English
  [Invited], [International presentation]
• Brown 氏の研究における余積構造の利用法: Hoffman 基底と深さ filtration
  安田 正大
  関西多重ゼータ研究集会（第１１回）, 22 Sep. 2012, Japanese
  [Invited], [Domestic Conference]
• 整係数 2 次元 p 進表現の構成
  安田 正大
  第 57 回代数学シンポジウム, 23 Aug. 2012, Japanese
  [Invited], [Domestic Conference]
• Bernstein center I, II
  Seidai Yasuda
  勉強会 「p 進代数群の表現論」, 17 Feb. 2012, Japanese
  [Invited], [Domestic Conference]
• Some hypergeometric polynomials and reductions of crystalline representations with moderate Hodge-Tate weights
  Seidai Yasuda
  Workshop on p-adic arithmetic geometry and motives, 25 Jan. 2012, English
  [Domestic Conference]
• Stability of a higher Chow group of an elliptic curve
  Seidai Yasuda
  Workshop on arithmetic geometry 2011, 12 Oct. 2011, English
  [Invited], [Domestic Conference]
• Euler 系とその応用について
  安田 正大
  北大数論幾何学セミナー, 06 Jan. 2011, Japanese
  [Invited], [Domestic Conference]
• Construction of extensions by $K_2$
  Seidai Yasuda
  第１３回白馬整数論オータムワークショップ「被覆群上の保型表現・保型形式」, 04 Nov. 2010, English
  [Invited], [International presentation]
• 安定跡公式と志村多様体
  安田 正大
  第18回整数論サマースクール「アーサー・セルバーグ跡公式入門」, 08 Sep. 2010, Japanese
  [Invited], [Domestic Conference]
• $GL(n)$のガロア表現と局所及び大域ラングランズ対応 (Introduction to Clozel, Harris-Taylor and Taylor-Yoshida)
  安田 正大
  $GSp(4)$ の数論を中心とした基礎的ワークショップ, 06 Aug. 2010, Japanese
  [Invited], [Domestic Conference]
• Iwasawa theory and higher Fitting ideals
  Seidai Yasuda
  Workshop on Iwasawa Theory over Function Fields of Characteristic $p>0$, 06 Apr. 2010, English
  [Invited], [International presentation]
• モジュラ曲線の直積のK_3元について
  安田 正大
  東北大学・代数セミナー, 14 Jan. 2010, Japanese
  [Invited], [Domestic Conference]

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  01 Apr. 2021 - 31 Mar. 2026
  安田 正大; 古庄 英和; 山下 剛
  本年度の研究代表者の主な研究実績は次の３つである：１．研究分担者の山下氏と共同で、p 進数のなす体を基礎体とする 2 次元クリスタリン表現の整格子を Wach 加群を用いて具体的に調べる共同研究の成果を精密に検討し、詳細を論文にまとめる作業を進めた。その結果、今まで得られていた結果を精密化することができ、特に tres ramifie と呼ばれる還元を持つ場合の構造を詳しく調べることができた。このことによって、2 次元クリスタリン局所変形環の構造が tres ramifie の場合にも詳しく調べることができると期待される。２．近藤智氏と共同で、非アルキメデス局所体上の中心斜体の既約許容表現についての局所新形式の理論を開拓した。特に、general と呼ばれる既約 smooth 表現のクラスについてはかなりまとまった結果をえることができ、成果を論文をまとめる作業を進めた。３．p 進体 Q_p の絶対ガロア群の外部自己同型のなす群を、Q_p の代数閉包上の有理数値関数で適当な条件のなす集合に埋め込むことに成功した。
  研究分担者の山下は、上記１．の共同研究に加え、次の２つの研究を行った。４．Heilbronn 仮想指標の理論を一般化した捻り Heilbronn 仮想指標の理論をつくった。５. 遠アーベル幾何学における p 進セクション予想についての研究を進めた。
  研究分担者の古庄は、KZ 結合子の視点から p 進超幾何関数の研究を行い、p 進長期化関数と p 進多重ポリログとの関係について調べた。
  日本学術振興会, 基盤研究(B), 北海道大学, 23K20782
• 数論的対象の背後にある幾何学の発見・構築を通じたL関数・ガロア表現の研究
  科学研究費助成事業 基盤研究(B)
  01 Apr. 2021 - 31 Mar. 2026
  安田 正大; 古庄 英和; 山下 剛
  日本学術振興会, 基盤研究(B), 北海道大学, 21H00969
• Strategic research to construct motivic units using new symmetry
  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (S)
  11 Jun. 2018 - 31 Mar. 2023
  坂内 健一; 志甫 淳; 寺杣 友秀; 勝良 健史; 小林 真一; 安田 正大; 山本 修司
  昨年までの研究経過を踏まえて、総実代数体に付随する代数トーラスに対してプレクティックDeligne-Beilinsonコホモロジーを定義して、その中にポリログを定義する研究に着手した。ポリログのde Rham実現を具体的に記述しようと試みた過程で、総実代数体のHecke L関数の負の整数点の値の母関数について、新谷卓郎が研究した非標準な母関数について、この母関数を、代数トーラスの同変コホモロジー類として解釈すると、極めて自然で標準的な類を構成できることを発見した。このコホモロジー類を「新谷生成類」と呼ぶことにした。通常、高次のコホモロジー類を点に制限すると消えてしまうが、同変コホモロジー類を考えることで「点での値」をうまく定義できることが新しい発見である。当初は、プレクティックポリログのホッジ実現を完全に書ききるまで、整数論的に面白い成果は得られないと想定していたが、早い段階で、整数論の基本的な結果に対して新しい知見を得たことは、とても嬉しく感じている。上記の結果を受けて、新谷生成類の考え方をベースに、総実代数体に付随するp進ポリログ関数の定義をした。これもやはり、総実代数体の代数トーラスの同変コホモロジー類として定義した。また、この関数の等分点での制限が、p進Hecke L関数の特殊値と一致することを証明した。この成果は、有理数体の場合のColemanの古典的な結果を総実代数体の場合に一般化するものであり、今後、今回の代数トーラスやp進ポリログ関数が数論幾何的予想に対して有用であることを強く示唆する結果である。
  Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (S), Keio University, 18H05233
• モチヴィックガロア群と多重ゼータ値から広がる数学ー整数論からの解放ー
  科学研究費助成事業 基盤研究(B)
  01 Apr. 2018 - 31 Mar. 2023
  古庄 英和; 田坂 浩二; 大野 泰生; 安田 正大
  7月にカナダのCRM研究所のプログラム「Expansions, Lie Algebras, and Invariants」に参加し、Enriquez氏と共同研究を続けRacinetが2002年に提出したdouble shuffle群のBetti側に対応する群の正体を明らかにした。1年前に発見した調和余積のBetti対応物を用いてde Rham側と同様な簡明な表示を与えることができた。この結果をpreprintにまとめ発表した。今までの「Double shufle関係式のBetti側の理論」に関する一連の共著論文（3本）をようやく書き終えたことになるが、読み直してみると複雑に入り組んでいた議論のいくつかが簡略化できそうなことに気づいたので、引き続き議論の整備をし改訂を行っていくことにした。
  11月には「多重ゼータ値の諸相」の国際集会を数理解析研究所で主催した。多重ゼータ値を研究する研究者を各方面から招聘した。Enriquez氏もこの集会に招聘し共同研究のサーベイ発表してもらった。
  研究分担者の田坂氏は楕円モジュラー形式の新形式を二重Eisenstein級数の基底で表示する明示公式を得た。大野氏はArakawa-Kaneko多重ゼータ関数の特殊値に関する和公式を構成した。安田氏はグラフの圏を適当に局所化することによって得られる対称性の観点から複シャッフル空間に関する Goncharovの仕事の再解釈を行なった。
  日本学術振興会, 基盤研究(B), 名古屋大学, 18H01110
• Adelic new methods on arithemetic geometry and their applications to p-adic Hodge theory and multiple L-functions
  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)
  01 Apr. 2015 - 31 Mar. 2020
  Yasuda Seidai
  The research representative and Go Yamashita have constructed families of Wach modules of rank two and applied them to the study of crystalline deformation rings of dimension two. He and Satoshi Kondo have constructed lifts of the zeta elements in motivic cohomologies of Drinfeld modular varieties to their integral models satisfying norm relations, and have constructed a theory of topoi related to monoids. He and Yusuke Sugiyama have introduced a new notion of pseudo-tameness and, by using them, have proved that any algebraic curve over an algebraically closed field has a tame morphism to the projective line. He has introduced the derived double shuffle spaces and has applied them to show a double shuffle analogue of Broadhurst-Kreimer conjecture in depth four. He has found that a suitable quotient of a Hilber modular surface related to the L-function of a certain curve of genus is a Kummer surface.
  Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (B), Osaka University, 15H03610
• Generalization of Iwasawa theory through Galois doformation and search for new phenomena
  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)
  01 Apr. 2014 - 31 Mar. 2020
  Ochiai Tadashi
  With this grant, I executed the following projects
  (I) Euler system thheory over deformation rings with singularity, (II) Iwasawa theory for GSp(4), (III) Iwasawa theory for Coleman families, (IV) Iwasawa theory for CM fields and CM modular forms, (V) functional equation of Selmer group in noncommutative Iwasawa theory, (VI) Euler system theory for higher rank Galois representation. Also, I organized an international workshop for the generalization of p-adic L-function.
  Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (B), Osaka University, 26287005
• Strategic Reseach using Eisensterin classes to prove Conjectures in Arithmetic Geometry
  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (A)
  01 Apr. 2014 - 31 Mar. 2019
  Bannai Kenichi; TAKAI Yuuki; OTA Kazuto; ONO Masataka; KIRAL Erin Mehmet
  Our original goal was to study the polylogarithm in the case of totally real fields. Our original goal was to study the polylogarithm via the Eisenstein class, but in course of our research, we realized the importance of a certain algebraic torus associated to a totally real field, and using the ideas from plectic structures proposed by Nekovar and Scholl, we succeeded in proving that the Shintani generating function which generates special values of Shintani zeta functions, defines a canonical class on the algebraic torus.
  Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (A), Keio University, 26247004
• A research on a new symmetry on motive with real multiplication
  Grants-in-Aid for Scientific Research Grant-in-Aid for Challenging Exploratory Research
  01 Apr. 2016 - 31 Mar. 2018
  kobayashi shinichi; OTA Kazuto; HAGIHAEA Kei; YAMADA Kazuki
  Plectic conjecture by J. Nekovar and A. Scholl is considered to give a strong impact on the study for motive with real multiplication if the program is completed. However, the program has just started. We studied the Hodge realization of the plectic cohomology. We gave an equivalent description of mixed plectic Hodge structures in terms of the weight and partial Hodge filtrations. We also constructed an explicit complex calculating the extension groups in this category. This result is important to consider applications to concrete problems.
  Japan Society for the Promotion of Science, Grant-in-Aid for Challenging Exploratory Research, Kyushu University, 16K13742
• Ramification theory of automorphic representations and arithmetic of special L-values
  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
  01 Apr. 2015 - 31 Mar. 2018
  Yoshi-Hiro Ishikawa
  Number theory investigation usually involves quite vast area of deep mathematics,like as the Fermat Last Theolem does. The Langlands Program, which led to the settlement of FLT, has been the central strategy of arithmetic since 70s. We follow the LP to study the ramification theory of the group U(3) representations in view point of L‐/ε‐factors. Our approach is resorting to integral presentations of L‐function of automorphic forms, whose ramified factors give us arithmetic info. The point is to find nice Whittaker functions appearing in the ramified factor. We can successfully detect where/which the nice ones are only in the case of Real/unramified U(3).
  Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), Okayama University, 15K04784
• Study of the moduli of Galois representations of number fields and function fields
  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
  01 Apr. 2013 - 31 Mar. 2016
  Taguchi Yuichiro; HATTORI Shin; KURIHARA Masato; SAITO Takeshi; TAMAGAWA Akio; YASUDA Seidai; HIRANOUCHI Toshiro
  We have constructed a moduli scheme of Galois representations and studied its properties, and obtained some basic results. We have also obtained several related results, such as: (1) a vanishing theorem of the Galois-fixed subspace of a Galois representation of a rather general type of complete discrete valuation field (a generalization of a theorem of Imai) and its application to Iwasawa theory, (2) a result on the congruence of Galois representations and its application to non-existence theorems a la Rasmussen-Tamagawa, (3) proof of the fact that the Hecke field of a geometric Galois represntation is often (say, with density 1 primes, in certain cases) generated by the trace of the Frobenius for a single finite prime, (4) an upper bound of the number of the connected components of the Zariski closure of the image of a Galois representation.
  Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), Kyushu University, 25400016
• Ramified components of automorphic representations: local theory and its application to special L-values
  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
  01 Apr. 2012 - 31 Mar. 2015
  ISHIKAWA YOSHI-HIRO; TSUZUKI Masao; YASUDA Seidai; TAKANO Keiji; MIYAUCHI Michitaka
  Number theory investigation usually involves quite vast area of deep mathematics, like as the Fermat Last Theolem does. The Langlands Program, which led to the settlement of FLT, has been the central strategy of arithmetic since 70s. We follow the LP to study the ramification theory of the group U(3) representations in view point of L-/ε-factors. Our approach is resorting to integralpresentations of L-function of automorphic forms, whose ramified factors give us arithmetic info. The point is to find nice Whittaker functions appearing in the ramified factor. We can successfully detect where/which the nice ones are in the case of Real/unramified U(3). As an application to the global problem, we got algebraicity result for all the critical values of twisted L-function of generic cuspidal representaions on U(3).
  Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), Okayama University, 24540021
• Study of various aspects of Galois representations
  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
  2010 - 2012
  TAGUCHI Yuichiro; SAITO Takeshi; HIRANOUCHI Toshiro; YASUDA Seidai; HATTORI Shin; MIEDA Yoichi
  We obtained several useful results on Galois representations. In particular, for a geometric Galois representation of a complete discrete valuation fields with imperfect residue field, we proved, under suitable conditions, that its fixed subspace over a ``large'' Kummer extension of the base field is trivial, and applied this to Iwasawa Theory. Moreover, we studied the congruence of Galois representations and obtained some results on the generalization of the Rasmussen-Tamagawa conjecture.
  Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), Kyushu University, 22540024
• Study onε-factor of automorphic representations and conductor of remified components
  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
  2009 - 2011
  ISHIKAWA Yoshihiro; MORIYAMA Tomonori; YASUDA Seidai; MIYAUCHI Michitaka; TAKANO Keiji
  Number theory investigation usually involves quite vast area of deep mathematics, like as the Fermat Last Theolem does. The Langlands Program, which led to the settlement of FLT, has been the central strategy of arithmetic since 70s. We follow the LP to study the ramification theory of the group U(3) representations in view point of L-/ε-factors. Our approach is resorting to integral presentations of L-function of automorphic forms, whose ramified factors give us arithmetic info. The point is to find nice Whittaker functions appearing in the ramified factor. We can successfully detect where/which the nice ones are in the case of Real/unramified U(3).
  Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), Okayama University, 21540017
• On the special values of the product of L-functions and the periods of automorphic forms defined over function fields
  Grants-in-Aid for Scientific Research Grant-in-Aid for Challenging Exploratory Research
  2009 - 2011
  KONDO Satoshi; YASUDA Seidai
  We verified that when an automorphic form over a function field is integrated over the maximal torus at a fixed prime, the value may be expressed in terms of special values of L-functions, when the function field is that of a projective line over a finite field. We were not able to verify this over the function field of a more general curve.
  Japan Society for the Promotion of Science, Grant-in-Aid for Challenging Exploratory Research, The University of Tokyo, 21654002
• Towards ramification theory of automorphic representations : Ramified representations and their L-factors
  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
  2007 - 2008
  ISHIKAWA Yoshihiro; MORIYAMA Tomonori; YASUDA Seidai; YOSHINO Yuji; TAKANO Keiji; WAKATSUKI Satoshi
  フェルマ予想(FLT)の様な数論の問題は, 非常に広範で深い理論を駆使して研究される。FLTの証明をも含み, 70年代より数論研究の支柱たり続けているLanglandsプログラムに沿って, 比較的小さい群U(3), GSp(4)の場合に, その分岐表現と付随するL-関数を研究した。方針は, L-関数を上の群を対称性にもつ保型形式という"関数"の積分変換で表示し, その積分の分岐因子を(一般化)ホイタッカー関数を通じて明示的に研究する。表現の分岐が激しくない簡易な場合に, L-因子を計算した。分岐が激しい場合にも, 部分群からのアプローチが有効で有ることが判った。
  Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), Okayama University, 19540032
• 数論多様体の分岐とL-関数に関する研究
  科学研究費助成事業 若手研究(B)
  2003 - 2005
  安田 正大
  1.近藤智氏との共同研究を行い、以下の成果を得た。
  前年度までの共同研究に登場した、正標数の大域体F,Fの素点∞、および正標数d【greater than or equal】1に対する、F上の階数dの、適当なレベル構造つきのDrinfeldモジュラー多様体のd-次Milnor K-群の元の改良および一般化を行い、Drinfeldモジュラー多様体の無限素点でのreductionと関係するBruhat-Tits buildingの数論的商に関する、GL_dの一般のモジュラーシンボル(の関数体類似)と関係づけることができた。
  まだ完成していないが、これらのモジュラーシンボルが、上記の数論的商のとあるホモロジー群を生成することが証明できる見通しが立っており、それが実元すると、Drinfeldモジュラー多様体のMilnor K-群に十分多くの元が構成できたことになる。
  またd=2の場合に、上記のように構成した元を用いて、関数体上の楕円曲線のK_<2->群に十分多くの元を作る事への応用を行った(プレプリント執筆中)。この方面へ応用するというアイディアは近藤氏による。当該研究者の貢献はl-進層の消滅サイクルの理論を援用して、曲線のモデルの考察を最小限にとどめる技法を開発したところにある。
  2.体上の楕円曲線EのK_1群とK_2群を、Gersten複体の部分複体を用いて記述する予想を与え、E上のベクトル束の分類およびFourier-向井変換を用いて、それを証明するための計算の主要な部分を実行した。
  日本学術振興会, 若手研究(B), 京都大学, 15740012
• 数論的多様体の分岐とL-関数
  科学研究費助成事業 特別研究員奨励費
  2002 - 2004
  安田 正大
  ArtinモチーフのTate twistに対するBloch加藤予想と関数等式とのcompatibilityについて研究した結果,それが(B^<ψ=p^γ>_∩B^+_)/Z_pt^γの構造を調べることに帰着された.Artinモチーフに対するBloch加藤予想と関数等式とのcompatibilityに関する下記の結果を,ChinbergのΩ(N/K,2)不変量に関する予想と関係づけられることがわかった.また(B^<ψ=p^γ>_∩B^+_)/Z_pt^γの構造をと,導手の理論との密接な結びつきが明らかになってきた.
  一咋年に自分が得た,局所Weil群の表現に対するε_0-因子の構成に関する結果が改良された,当時の結果では,係数環が剰余体が代数閉体の局所環であって,p-乗写像が全射となるものに対してしか,ε_0-定数が構成されていなかった.が、加法指標の値域を係数環と分離することにより,pが加逆となる,一般の可換noether環を係数環とする表現に対しても,同様にε_0-因子の理論が作れることがわかった.
  加藤和也氏により構成されているp-進ε-元の(ψ,Γ)-加群の視点からの見直しを行った結果,rank 1の表現に対する加藤氏のp-進ε-元は,一見Coleman巾級数を用いた,技巧的な方法を用いて構成されているように見えるが,(ψ,Γ)-加群の立場から見ると,p-進ε-元は,固定した1のp-巾根のsystem ε=(ζ_)から作られる元[ε]∈Aに1∈Q_pを送ることにより得られるアーベル群の準同型Q_p→A^×を,通常の加法指標の類似と思い,Tateによるε-因子の構成と同様の構成を実施して構成したものである,という自然な見方ができることがわかった.
  係数をp-加逆な局所環に一般化したところでの,Langlands対応の問題は,定式化をすることがまず困難であるという問題があることがわかった.不分岐なところで考えると,表現そのものではなく,表現行列の固有多項式しか問題にしていない感が強い.Tameの部分に何らかの対応らしいものを見出すことが勝負だと思われる.ε-因子はそもそも表現行列の固有多項式にしか依存しないことも判明した.
  対応の確立のためには,tameな場合が本質的であると思われるが,それには,Bushnell, Kutzkoのtypeの理論を用いた,ε-因子の構成の理論(Bushnell, Henniart)と,自分のε_0-元の構成との関連をもっと追う必要があろう.
  日本学術振興会, 特別研究員奨励費, 京都大学, 02J07379