Researcher Database

Masanori Asakura
Faculty of Science Mathematics Mathematics
Professor

Researcher Profile and Settings

Affiliation

  • Faculty of Science Mathematics Mathematics

Job Title

  • Professor

Research funding number

  • 60322286

J-Global ID

Research Interests

  • ホッジ理論   L functions   p-adic special functions   periods of integrals   regulators   

Research Areas

  • Natural sciences / Algebra / Arithmetic Geometry

Academic & Professional Experience

  • 2008/04 - Today Hokkaido university

Research Activities

Published Papers

  • Regulators of K_2 of hypergeometric fibrations
    ASAKURA Masanori
    Res. Number Theory 4 (2) 2018 [Refereed][Not invited]
  • CM regulators and hypergeometric functions, II
    ASAKURA Masanori, OTSUBO Noriyuki
    Math. Z. 289 (3-4) 1325 - 1355 2018 [Refereed][Not invited]
  • CM periods, CM regulators and hypergeometric functions, I.
    ASAKURA Masanori, OTSUBO Noriyuki
    Canad. J. Math. 70 (3) 481 - 514 2018 [Refereed][Not invited]
  • A simple construction of regulator indecomposable higher Chow cycles in elliptic surfaces
    ASAKURA Masanori
    London Math. Soc. Lecture Note Ser. 427 231 - 240 2016 [Refereed][Not invited]
  • Rob De Jeu, James D. Lewis, Masanori Asakura
    Journal of K-Theory 11 (2) 243 - 282 1865-2433 2013/04 [Refereed][Not invited]
     
    Let U/C be a smooth quasi-projective variety of dimension d, CHr (U,m) Bloch's higher Chow group, and cl r,m: CHr (U,m) âŠ-â"š → homMHS (â"š(0), H 2r-m (U, â"š(r))) the cycle class map. Beilinson once conjectured cl r,m to be surjective [Be] however, Jannsen was the first to find a counterexample in the case m = 1 [Ja1]. In this paper we study the image of cl r,m in more detail (as well as at the generic point of U) in terms of kernels of Abel-Jacobi mappings. When r = m, we deduce from the Bloch-Kato conjecture (now a theorem) various results, in particular that the cokernel of cl m,m at the generic point is the same for integral or rational coefficients. © 2013 ISOPP.
  • ASAKURA Masanori, SATO Kanetomo
    J. Algebraic Geom. 22 (3) 481 - 547 2013 [Refereed][Not invited]
  • Quintic surface over p-adic local fields with infinite p-primary torsion in the Chow group of 0-cycles
    ASAKURA Masanori
    Contemp. Math. 571 1 - 17 2012 [Refereed][Not invited]
  • Beilinson's Tate conjecture for K_2 of elliptic surface:survey and examples
    ASAKURA Masanori, SATO Kanetomo
    Cycles, Motives and Shimura Varieties 35 - 58 2010 [Refereed][Not invited]
  • Local units are generated by certain cyclotomic units
    ASAKURA Masanori
    RIMS Kokyuroku B12 183 - 191 2009 [Refereed][Not invited]
  • Masanori Asakura, Shuji Saito
    MATHEMATISCHE ANNALEN 341 (1) 169 - 199 0025-5831 2008/05 [Refereed][Not invited]
     
    We discuss the Noether-Lefschetz locus for Beilinson's Hodge cycles on the complement of two or three hyperplane sections in a smooth projective surface in P-3. The main theorem gives an explicit description of maximal components of the Noether-Lefschetz locus.
  • Masanori Asakura
    INVENTIONES MATHEMATICAE 172 (1) 213 - 229 0020-9910 2008/04 [Refereed][Not invited]
  • Masanori Asakura, Shuji Saito
    ALGEBRA & NUMBER THEORY 1 (2) 163 - 181 1937-0652 2007 [Refereed][Not invited]
     
    We give an example of a projective smooth surface X over a p-adic field K such that for any prime l different from p, the l-primary torsion subgroup of CH(0)(X), the Chow group of 0-cycles on X, is infinite. A key step in the proof is disproving a variant of the Bloch-Kato conjecture which characterizes the image of an l-adic regulator map from a higher Chow group to a continuous etale cohomology of X by using p-adic Hodge theory. With the aid of the theory of mixed Hodge modules, we reduce the problem to showing the exactness of the de Rham complex associated to a variation of Hodge structure, which is proved by the infinitesimal method in Hodge theory. Another key ingredient is the injectivity result on the cycle class map for Chow group of 1-cycles on a proper smooth model of X over the ring of integers in K, due to K. Sato and the second author.
  • Beilinson's Hodge Conjecture with Coefficients
    ASAKURA Masanori, SAITO Shuji
    London Math. Soc. Lecture Note Ser. 344 3 - 37 2007 [Refereed][Not invited]
  • Masanori Asakura
    INVENTIONES MATHEMATICAE 165 (2) 267 - 324 0020-9910 2006/08 [Refereed][Not invited]
  • M Asakura, S Saito
    MATHEMATISCHE ZEITSCHRIFT 252 (2) 251 - 273 0025-5874 2006/02 [Refereed][Not invited]
     
    We discuss the Noether-Lefschetz locus for Beilinson's Hodge cycles. Here ``Beilinson's Hodge cycles'' mean the cohomology class of Bloch's higher Chow cycles on smooth varieties. The main result is to give an estimate of the dimension of the maximal component of the Noether-Lefschetz locus for the universal family of open complete intersections.
  • M Asakura, S Saito
    MATHEMATISCHE NACHRICHTEN 279 (1-2) 5 - 37 0025-584X 2006 [Refereed][Not invited]
     
    In this paper, we develop the theory of Jacobian rings of open complete intersections, which are pairs (X,Z) where X is a smooth complete intersection in the projective space and Z is a simple normal crossing divisor in X whose irreducible components are smooth hypersurface sections on X. Our Jacobian rings give an algebraic description of the cohomology of the open complement X - Z and it is a natural generalization of the Poincare residue representation of the cohomology of a hypersurface originally invented by Griffiths. The main results generalize Macaulay's duality theorem and Donagi's symmetrizer lemma for usual Jacobian rings for hyper-surfaces. A feature that distinguishes our generalized Jacobian rings from usual ones is that there are instances where duality fails to be perfect while the defect can be controlled explicitly by using the defining equations of Z in X. Two applications of the main results are given: One is the infinitesimal Torelli problem for open complete intersections. Another is an explicit bound for Nori's connectivity in case of complete intersections. The results have been applied also to study of algebraic cycles in several other works. (c) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
  • A criterion of exactness of the Clemens-Schmid
    ASAKURA Masanori
    Osaka J. Math. 40 (4) 977 - 980 2003 [Refereed][Not invited]
  • M Asakura
    K-THEORY 27 (3) 273 - 280 0920-3036 2002/11 [Refereed][Not invited]
     
    We construct 0-cycles on a self-product of a curve whose cycle classes are linearly independent in the extension group of an arithmetic Hodge structure. This is an extended version of Theorem 4.5 of Asakura's contribution to CMR Lecture Notes Ser. 24 (( 2000), pp. 133-154).
  • M Asakura
    INVENTIONES MATHEMATICAE 149 (3) 661 - 685 0020-9910 2002/09 [Refereed][Not invited]
  • Motives and algebraic de Rham cohomology
    Masanori Asakura
    CRM proceedings and Lecture Notes 24 133 - 154 2000 [Refereed][Not invited]
  • K Matsumi, K Sato, M Asakura
    K-THEORY 18 (3) 203 - 234 0920-3036 1999/11 [Refereed][Not invited]
     
    The reciprocity map of a smooth proper variety over a finite field is known to have a trivial kernel and dense image. In this paper, we investigate the reciprocity map of a normal surface proper over a finite field and give two examples of normal projective surfaces whose reciprocity maps are not injective.
  • Regulator of Hypergeometric Fibrations
    ASAKURA Masanori, OTSUBO Noriyuki
    To appear in Proc. of Conferences "Regulators IV" [Refereed][Not invited]
  • An Algebro-geometric study of special values of hypergeometric functions 3F2
    ASAKURA Masanori, OTSUBO Noriyuki, TERASOMA Tomohide
    To appear in Nagoya Math. J. [Refereed][Not invited]
  • A functional logarithmic formula for the hypergeometric function 3F2
    ASAKURA Masanori, OTSUBO Noriyuki
    To appear in Nagoya Math. J. [Refereed][Not invited]

Conference Activities & Talks

  • F-isocrystal and p-adic regulators via hypergeometric functions  [Invited]
    ASAKURA Masanori
    Hakodate workshop in arithmetic geometry 2017  2017/05  函館
  • F-isocrystal and p-adic regulators via hypergeometric functions  [Invited]
    ASAKURA Masanori
    代数・解析・幾何学セミナー  2017/02  鹿児島大学
  • Regulagtors on hypergeometric fibrations  [Invited]
    ASAKURA Masanori
    Motives and Complex Multiplication  2016/08  アスコナ(スイス)
  • Regulators of hypergeometric fibrations  [Invited]
    ASAKURA Masanori
    Arithmetic L-functions and Differential Geometric Methds  2016/05  パリ大学
  • The period conjecture of Gross-Deligne for fibrations  [Invited]
    ASAKURA Masanori
    Arithmetic and Algebraic Geometry 2015  2015/01
  • Period and regulator for fibrations with CM structure  [Invited]
    ASAKURA Masanori
    Motives in Tokyo  2014/12  東京大学
  • Period and regulator for fibrations with CM structure  [Invited]
    ASAKURA Masanori
    Cohomological Realization of Motives  2014/12  バンフ(カナダ)
  • Real regulator on K_1 of a fibration of curves  [Invited]
    ASAKURA Masanori
    Recent advances in Hodge theory: period domains, algebraic cycles, and arithmetic  2013/06  ブリティッシュコロンビア大学
  • Syntomic regulator on elliptic fibrations  [Invited]
    ASAKURA Masanori
    Algebraic K-theory and Its Applications  2011/03  南京大学
  • K_2 のTate 予想とp進レギュレーター  [Invited]
    朝倉 政典
    日本数学会秋季総合会  2009/09  大阪大学

Educational Activities

Teaching Experience

  • Linear Algebra I
    開講年度 : 2018
    課程区分 : 学士課程
    開講学部 : 全学教育
    キーワード : 行列, 連立1次方程式, 基本変形, 階数, 行列式, 逆行列
  • Linear Algebra II
    開講年度 : 2018
    課程区分 : 学士課程
    開講学部 : 全学教育
    キーワード : ベクトル空間, 線形写像, 線形独立, 基底, 固有値, 固有ベクトル, 対角化
  • Exercises on Basic Algebra
    開講年度 : 2018
    課程区分 : 学士課程
    開講学部 : 理学部
    キーワード : 代数系,同値関係,剰余類,群,部分群,正規部分群,剰余群,準同型定理,環,イデアル,剰余環,素イデアル,極大イデアル,整域,体,標数,体の拡大
  • Special Lecture on Mathematics
    開講年度 : 2018
    課程区分 : 学士課程
    開講学部 : 理学部
    キーワード : 計算機代数,計算機数論,数式処理システム


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