研究者データベース

朝倉 政典(アサクラ マサノリ)
理学研究院 数学部門 数学分野
教授

基本情報

所属

  • 理学研究院 数学部門 数学分野

職名

  • 教授

学位

  • 博士(数理科学)(東京大学)

科研費研究者番号

  • 60322286

J-Global ID

研究キーワード

  • ホッジ理論   L関数   p進特殊関数   周期積分   レギュレーター   

研究分野

  • 自然科学一般 / 代数学 / 数論幾何学

職歴

  • 2008年04月 - 現在 北海道大学大学院理学研究院

研究活動情報

論文

  • Regulators of K_2 of hypergeometric fibrations
    朝倉 政典
    Res. Number Theory 4 2 2018年 [査読有り][通常論文]
  • CM regulators and hypergeometric functions, II
    朝倉政典, 大坪紀之
    Math. Z. 289 3-4 1325 - 1355 2018年 [査読有り][通常論文]
  • CM periods, CM regulators and hypergeometric functions, I.
    朝倉政典, 大坪紀之
    Canad. J. Math. 70 3 481 - 514 2018年 [査読有り][通常論文]
  • A simple construction of regulator indecomposable higher Chow cycles in elliptic surfaces
    朝倉 政典
    London Math. Soc. Lecture Note Ser. 427 231 - 240 2016年 [査読有り][通常論文]
  • Rob De Jeu, James D. Lewis, Masanori Asakura
    Journal of K-Theory 11 2 243 - 282 2013年04月 [査読有り][通常論文]
     
    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.
  • 朝倉政典, 佐藤周友
    J. Algebraic Geom. 22 3 481 - 547 2013年 [査読有り][通常論文]
  • Quintic surface over p-adic local fields with infinite p-primary torsion in the Chow group of 0-cycles
    朝倉 政典
    Contemp. Math. 571 1 - 17 2012年 [査読有り][通常論文]
  • Beilinson's Tate conjecture for K_2 of elliptic surface:survey and examples
    朝倉政典, 佐藤周友
    Cycles, Motives and Shimura Varieties 35 - 58 2010年 [査読有り][通常論文]
  • Local units are generated by certain cyclotomic units
    朝倉 政典
    京都大学数理解析研究所講究録別冊 B12 183 - 191 2009年 [査読有り][通常論文]
  • Masanori Asakura, Shuji Saito
    MATHEMATISCHE ANNALEN 341 1 169 - 199 2008年05月 [査読有り][通常論文]
     
    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 2008年04月 [査読有り][通常論文]
  • Masanori Asakura, Shuji Saito
    ALGEBRA & NUMBER THEORY 1 2 163 - 181 2007年 [査読有り][通常論文]
     
    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
    朝倉政典, 斎藤秀司
    London Math. Soc. Lecture Note Ser. 344 3 - 37 2007年 [査読有り][通常論文]
  • Masanori Asakura
    INVENTIONES MATHEMATICAE 165 2 267 - 324 2006年08月 [査読有り][通常論文]
  • M Asakura, S Saito
    MATHEMATISCHE ZEITSCHRIFT 252 2 251 - 273 2006年02月 [査読有り][通常論文]
     
    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 2006年 [査読有り][通常論文]
     
    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
    朝倉 政典
    Osaka J. Math. 40 4 977 - 980 2003年 [査読有り][通常論文]
  • M Asakura
    K-THEORY 27 3 273 - 280 2002年11月 [査読有り][通常論文]
     
    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 2002年09月 [査読有り][通常論文]
  • Motives and algebraic de Rham cohomology
    朝倉 政典
    CRM proceedings and Lecture Notes 24 133 - 154 2000年 [査読有り][通常論文]
  • K Matsumi, K Sato, M Asakura
    K-THEORY 18 3 203 - 234 1999年11月 [査読有り][通常論文]
     
    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
    朝倉政典, 大坪紀之
    To appear in Proc. of Conferences "Regulators IV" [査読有り][通常論文]
  • An Algebro-geometric study of special values of hypergeometric functions 3F2
    朝倉政典, 大坪紀之, 寺杣友秀
    To appear in Nagoya Math. J. [査読有り][通常論文]
  • A functional logarithmic formula for the hypergeometric function 3F2
    朝倉政典, 大坪紀之
    To appear in Nagoya Math. J. [査読有り][通常論文]

講演・口頭発表等

  • F-isocrystal and p-adic regulators via hypergeometric functions  [招待講演]
    朝倉 政典
    Hakodate workshop in arithmetic geometry 2017 2017年05月 口頭発表(一般) 函館
  • F-isocrystal and p-adic regulators via hypergeometric functions  [招待講演]
    朝倉 政典
    代数・解析・幾何学セミナー 2017年02月 鹿児島大学
  • Regulagtors on hypergeometric fibrations  [招待講演]
    朝倉 政典
    Motives and Complex Multiplication 2016年08月 口頭発表(一般) アスコナ(スイス)
  • Regulators of hypergeometric fibrations  [招待講演]
    朝倉 政典
    Arithmetic L-functions and Differential Geometric Methds 2016年05月 パリ大学
  • The period conjecture of Gross-Deligne for fibrations  [招待講演]
    朝倉 政典
    Arithmetic and Algebraic Geometry 2015 2015年01月
  • Period and regulator for fibrations with CM structure  [招待講演]
    朝倉 政典
    Motives in Tokyo 2014年12月 東京大学
  • Period and regulator for fibrations with CM structure  [招待講演]
    朝倉 政典
    Cohomological Realization of Motives 2014年12月 バンフ(カナダ)
  • Real regulator on K_1 of a fibration of curves  [招待講演]
    朝倉 政典
    Recent advances in Hodge theory: period domains, algebraic cycles, and arithmetic 2013年06月 ブリティッシュコロンビア大学
  • Syntomic regulator on elliptic fibrations  [招待講演]
    朝倉 政典
    Algebraic K-theory and Its Applications 2011年03月 南京大学
  • K_2 のTate 予想とp進レギュレーター  [招待講演]
    朝倉 政典
    日本数学会秋季総合会 2009年09月 口頭発表(招待・特別) 大阪大学

教育活動情報

主要な担当授業

  • 線形代数学Ⅰ
    開講年度 : 2018年
    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
  • 線形代数学Ⅱ
    開講年度 : 2018年
    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
  • 代数学基礎演習
    開講年度 : 2018年
    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
  • 数学特別講義
    開講年度 : 2018年
    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


Copyright © MEDIA FUSION Co.,Ltd. All rights reserved.