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Adelic new methods on arithemetic geometry and their applications to p-adic Hodge theory and multiple L-functions

Research Project

Project/Area Number 15H03610
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionOsaka University

Principal Investigator

Yasuda Seidai  大阪大学, 理学研究科, 准教授 (90346065)

Co-Investigator(Kenkyū-buntansha) 古庄 英和  名古屋大学, 多元数理科学研究科, 教授 (60377976)
山下 剛  京都大学, 数理解析研究所, 講師 (70444453)
岩成 勇  東北大学, 理学研究科, 准教授 (70532547)
Project Period (FY) 2015-04-01 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥9,360,000 (Direct Cost: ¥7,200,000、Indirect Cost: ¥2,160,000)
Fiscal Year 2019: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2018: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2015: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Keywordsガロア表現 / p 進 Hodge 理論 / 関数体の数論 / 標数2の代数曲線 / 多重ゼータ値 / トポスの理論 / Fermat 曲線 / Kummer 曲面 / モジュラーシンボル / L関数 / 絶対ガロア群 / p進Hodge理論 / p進Hodge理論 / p進表現 / 複シャッフル / 結合子 / Grothendieck位相 / 複シャッフル空間 / サイトの理論 / Wach加群 / Belyi の定理 / 馴分岐 / Euler 系 / Drinfeld モジュラー多様体 / 代数学 / 整数論 / p進ホッジ理論 / イプシロン因子 / Grothendieck 位相 / サイト
Outline of Final Research Achievements

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.

Academic Significance and Societal Importance of the Research Achievements

上に述べた通り研究成果は多岐にわたっているが、いずれも整数論の当該分野の研究において、超幾何多項式、トポスの理論、pseudo-tame関数の概念、高次複シャッフル空間の考察など、新しい手法を用いて従来であまり進展がなかった方向への結果を得ているという点が画期的である。また、特別な種数2の代数曲線のL関数についての成果は限定的なものであるが、regulator 写像と L 関数の特殊値の関係の幾何的理解に役立ち、わかっている場合の少ない Beilinson 予想の進展に役立つと期待される。

Report

(6 results)
  • 2019 Annual Research Report   Final Research Report ( PDF )
  • 2018 Annual Research Report
  • 2017 Annual Research Report
  • 2016 Annual Research Report
  • 2015 Annual Research Report
  • Research Products

    (49 results)

All 2020 2019 2018 2017 2016 2015

All Journal Article (11 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 11 results,  Acknowledgement Compliant: 1 results,  Open Access: 2 results) Presentation (37 results) (of which Int'l Joint Research: 19 results,  Invited: 35 results) Book (1 results)

  • [Journal Article] Belyi's theoerm in characteristic two2020

    • Author(s)
      Yusuke Sugiyama, Seidai Yasuda
    • Journal Title

      Compositio Mathematica

      Volume: 156 Issue: 2 Pages: 325-339

    • DOI

      10.1112/s0010437x19007723

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Regularity of quotients of Drinfeld modular schemes2020

    • Author(s)
      Satoshi Kondo, Seidai Yasuda
    • Journal Title

      Pacific Journal of Mathematics

      Volume: 304 Issue: 2 Pages: 481-503

    • DOI

      10.2140/pjm.2020.304.481

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] First and second K-groups of an elliptic curve over a global field of positive characteristic2018

    • Author(s)
      Satoshi Kondo, Seidai Yasuda
    • Journal Title

      Annales de l'Institut Fourier

      Volume: 68, no. 5 Issue: 5 Pages: 2005-2067

    • DOI

      10.5802/aif.3202

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Sites whose topoi are the smooth representations of locally prodiscrete monoids2018

    • Author(s)
      Satoshi Kondo, Seidai Yasuda
    • Journal Title

      Journal of Algebra

      Volume: 502 Pages: 382-496

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Desingularization of complex multiple zeta-functions2017

    • Author(s)
      Hidekazu Furusho, Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura
    • Journal Title

      American Journal of Mathemtaics

      Volume: 139 Issue: 1 Pages: 147-173

    • DOI

      10.1353/ajm.2017.0002

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Fundamentals of p-adic multiple L-functions and evaluation of their special values2017

    • Author(s)
      Hidekazu Furusho, Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura
    • Journal Title

      Selecta Mathematica

      Volume: 23 Issue: 1 Pages: 39-100

    • DOI

      10.1007/s00029-016-0233-2

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] The radius of convergence of the p-adic sigma function2016

    • Author(s)
      Kenichi Bannai, Shinichi Kobayashi, Seidai Yasuda
    • Journal Title

      Mathematische Zeitschrift

      Volume: 印刷中 Issue: 1-2 Pages: 751-781

    • DOI

      10.1007/s00209-016-1783-x

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] A small remark on the filtered $\phi$-module of Fermat varieties and Stickelberger's theorem2016

    • Author(s)
      Go Yamashita
    • Journal Title

      Tsukuba J. Math.

      Volume: 40 Issue: 1 Pages: 119-124

    • DOI

      10.21099/tkbjm/1474747490

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Finite real multiple zeta values generate the whole space Z2016

    • Author(s)
      Seidai Yasuda
    • Journal Title

      International Journal of Number Theory

      Volume: 12 Issue: 03 Pages: 787-812

    • DOI

      10.1142/s1793042116500512

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On two higher Chow groups of schemes over a finite field2015

    • Author(s)
      Satoshi Kondo, Seidai Yasuda
    • Journal Title

      Documenta Mathematica

      Volume: 20 Pages: 737-752

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Tannakization in derived algebraic geometry2015

    • Author(s)
      Isamu Iwanari
    • Journal Title

      Journal of K-theory

      Volume: 14 Pages: 642-700

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Presentation] Vincent Lafforgue による関数体の Langlands 対応の構成2019

    • Author(s)
      安田 正大
    • Organizer
      代数的整数論とその周辺
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] Integral structures of two dimensional crystalline representations2019

    • Author(s)
      Seidai Yasuda
    • Organizer
      p-adic methods in arithmetic geometry at Sendai
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Cotangent complex and Postnikov towers2019

    • Author(s)
      Seidai Yasuda
    • Organizer
      Yatsugatake Workshop
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Depth graded structures2019

    • Author(s)
      Seidai Yasuda
    • Organizer
      Multiple zeta values and related topics
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [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2019

    • Author(s)
      安田 正大
    • Organizer
      早稲田大学整数論セミナー
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] On a relation of Hirose and Sato, Workshop: Multiple zeta values and related topics2019

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Multiple zeta values and related topics
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Modular complexes and dimensions of derived double shuffle modules2018

    • Author(s)
      安田 正大
    • Organizer
      第17回北陸数論研究集会
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] A product of Eisenstein series and special L-values over the rational function field2018

    • Author(s)
      Seidai Yasuda
    • Organizer
      NTCS Seminar on Number Theory
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Derived double shuffle Lie algebra and the Steinberg modules2018

    • Author(s)
      Seidai Yasuda
    • Organizer
      NTCS Seminar on Number Theory
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Foliations I, II2018

    • Author(s)
      Seidai Yasuda
    • Organizer
      八ヶ岳ワークショップ, 2018 The conservative conjecture
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 「p進多重ゼータ値」から「有限多重ゼータ値」へ2018

    • Author(s)
      安田 正大
    • Organizer
      第26回整数論サマースクール「多重ゼータ値」
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Reductions of Crystalline Representations and Hypergeometric Polynomials2018

    • Author(s)
      Go Yamashita
    • Organizer
      Pan Asia Number Theory Conference 2018
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On a relation of Hirose and Sato2018

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Taiwan-Japan Joint Workshop on Multiple Zeta Values
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] A Betti counterpart of the harmonic coproduct (I)2018

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Periods and Regulators
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Periond mappings for noncommutative algebras2018

    • Author(s)
      Isamu Iwanari
    • Organizer
      Lectures on higher structures and quantizations
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] pseudo-tame rational functions on curves in characteristic two2017

    • Author(s)
      Seidai Yasuda
    • Organizer
      Weekly Seminar of the Laboratory of Algebraic Geometry and its Applications
    • Place of Presentation
      National Research University Higher School of Economics, Moscow, Russia
    • Year and Date
      2017-03-22
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] On coefficients of Alekseev-Torossian associator2017

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Seminnaire Quantique
    • Place of Presentation
      IRMA, Strasbourg, France
    • Year and Date
      2017-03-20
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Ihara bracket for group schemes2017

    • Author(s)
      Seidai Yasuda
    • Organizer
      Low dimensional topology and number theory IX
    • Place of Presentation
      九州大学産学官連携イノベーションプラザ
    • Year and Date
      2017-03-16
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Linearized and derived double shuffle Lie algebras2017

    • Author(s)
      Seidai Yasuda
    • Organizer
      Workshop: Johnson homomorphisms and related topics
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Drinfeld modular 多様体上の zeta 元について2017

    • Author(s)
      安田正大
    • Organizer
      九大数理談話会
    • Related Report
      2017 Annual Research Report
  • [Presentation] 結合子と結合子関係式2017

    • Author(s)
      安田正大
    • Organizer
      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」
    • Related Report
      2017 Annual Research Report
  • [Presentation] Belyi's theorem in characteristic two2016

    • Author(s)
      Seidai Yasuda
    • Organizer
      p-adic methods in arithmetic geometry at Sendai, 2016
    • Place of Presentation
      東北大学
    • Year and Date
      2016-10-31
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] A stabilizer interpretation of the double shuffle Lie algebra2016

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Workshop on Grothendieck-Teichmuller Theories
    • Place of Presentation
      Chern Institute of Mathematics, Nankai University, Tianjin, China
    • Year and Date
      2016-07-29
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] IUTchIII-IV with remarks on the function-theoretic roots of the theory2016

    • Author(s)
      Go Yamashita
    • Organizer
      Inter-universal Teichmuller Theory Summit 2016
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2016-07-26
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Etale theta functions, mono-theta environments, and [IUTchI] §1 - §3 I, II2016

    • Author(s)
      Seidai Yasuda
    • Organizer
      Inter-universal Teichmuller Theory Summit 2016
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2016-07-19
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Complex and p-adic multiple zeta functions2016

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Low dimensional topology and number theory VIII
    • Place of Presentation
      IMAQ Seminar Room, Innovation Plaza, Fukuoka
    • Year and Date
      2016-03-25
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Topics on multiple zeta values2015

    • Author(s)
      Seidai Yasuda
    • Organizer
      NCTS Number Theory Seminar
    • Place of Presentation
      National Tsing Hua University (中華民国)
    • Year and Date
      2015-12-22
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Galois action on knots2015

    • Author(s)
      Hidekazu Furusho
    • Organizer
      代数的整数論とその周辺
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2015-12-03
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] p-adic multiple L-functions and p-adic multiple polylogarithms2015

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Zeta Functions of Several Variables and Applications
    • Place of Presentation
      名古屋大学
    • Year and Date
      2015-11-11
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Reconstructing schemes and Deligne-Mumford from derived infinitiy-categories2015

    • Author(s)
      Isamu Iwanari
    • Organizer
      Algebra seminar at Fudan University
    • Place of Presentation
      Fudan University (中華人民共和国)
    • Year and Date
      2015-11-06
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Derived algebraic geometry and Tannaka duality2015

    • Author(s)
      Isamu Iwanari
    • Organizer
      Colloquium at Fudan University
    • Place of Presentation
      Fudan University (中華人民共和国)
    • Year and Date
      2015-11-05
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] モチフィック多重ゼータ値と有限多重ゼータ値2015

    • Author(s)
      安田 正大
    • Organizer
      日本数学会2015年度秋季総合分科会
    • Place of Presentation
      京都産業大学
    • Year and Date
      2015-09-16
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Motivic and finite multiple zeta values2015

    • Author(s)
      Seidai Yasuda
    • Organizer
      Bousfield localizations form a set: a workshop in memory of Tetsusuke Ohkawa
    • Place of Presentation
      名古屋大学
    • Year and Date
      2015-08-30
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] From Bousfield localizations to dualities of tannakian type2015

    • Author(s)
      Isamu Iwanari
    • Organizer
      Bousfield localizations form a set: a workshop in memory of Tetsusuke Ohkawa
    • Place of Presentation
      名古屋大学
    • Year and Date
      2015-08-30
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 階数 2 の Wach加群の族の構成2015

    • Author(s)
      安田 正大
    • Organizer
      九大代数学セミナー
    • Place of Presentation
      九州大学
    • Year and Date
      2015-06-12
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Grids and the associated monoids2015

    • Author(s)
      安田 正大
    • Organizer
      上智大学数学談話会
    • Place of Presentation
      上智大学
    • Year and Date
      2015-05-22
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Integrality of p-adic multiple zeta values and application to finite multiple zeta values2015

    • Author(s)
      Seidai Yasuda
    • Organizer
      東京北京パリ数論幾何セミナー
    • Place of Presentation
      東京大学
    • Year and Date
      2015-04-08
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Book] 結び目とGrothendieck-Teichmuller群2016

    • Author(s)
      古庄英和著 ; 小谷久寿, 新甫洋史記述
    • Total Pages
      111
    • Publisher
      九州大学マス・フォア・インダストリ研究所
    • Related Report
      2015 Annual Research Report

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Published: 2015-04-16   Modified: 2022-11-04  

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