• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Arithmetic geometric approach for period integrals

Research Project

Project/Area Number 20540010
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionThe University of Tokyo

Principal Investigator

TERASOMA Tomohide  The University of Tokyo, 大学院・数理科学研究科, 教授 (50192654)

Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords周期積分 / モチーフ / 代数的サイクル / ホッジ構造 / 保型形式 / L関数 / 高次チャウ群 / バー構成
Research Abstract

We study period integrals of algebraic varieties from the view point of algebraic correspondence, algebraic cycles and special functions such as automorphic functions. By applying the method of bar construction to algebraic varieties over positive characteristic base field, we describe their p-fundamental group, and establish a basic tools for Hodge realization functors using Deligne differential graded algebras. We also prove some part of Beilinson conjectures concerning mixed elliptic motives. Concerning automorphic functions, we stablish several new Thomae type theorems related to K3 surfaces, etc.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (28 results)

All 2011 2010 2009 2008 Other

All Journal Article (9 results) (of which Peer Reviewed: 4 results) Presentation (16 results) Remarks (3 results)

  • [Journal Article] Algebraic correspondences between genus three curves and certain Calabi-yau varieties2010

    • Author(s)
      TERASOMA T.
    • Journal Title

      Amer.J.Math. 132 no.1

      Pages: 181-200

    • Related Report
      2010 Final Research Report
  • [Journal Article] Arithmetic geometric means for hyperelliptic curves and Calabi-Yau varieties2010

    • Author(s)
      MATSUMOTO K.-TERASOMA T.
    • Journal Title

      Internat.J.Math. 21 no.7

      Pages: 939-949

    • Related Report
      2010 Final Research Report
  • [Journal Article] The Artin-Schreier DGA and the Fp fundamental group of an Fp scheme, to appear from Proceedings of International conference Tata Institute2010

    • Author(s)
      TERASOMA T.
    • Journal Title

      Cycles, motives and Shimura varieties, Tata Institute of Fundamental Research

    • Related Report
      2010 Final Research Report
  • [Journal Article] DG-category and simplicial bar complex2010

    • Author(s)
      TERASOMA T.
    • Journal Title

      Mosc.Math.J. 10 no.1

      Pages: 231-267

    • Related Report
      2010 Final Research Report
  • [Journal Article] The Artin-Schreier DGA and the F_p-fundamental group ofan F_p-scheme2010

    • Author(s)
      Terasoma, T.
    • Journal Title

      Proceedings of the international Colloquium on Cycles, Motives and Shimura varieties

      Pages: 493-530

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Arithmetic-geometric means for hyperelliptic curves and Calabi-Yau varieties2010

    • Author(s)
      Matsumoto, K.Terasoma, T.
    • Journal Title

      Internat.J.Math.

      Volume: 21 Pages: 939-949

    • Related Report
      2010 Annual Research Report 2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Jacobi's formula for Hesse cubic curves.2010

    • Author(s)
      Matsumoto, K.Terasoma, T.Yamazaki, S.
    • Journal Title

      Acta Math.Vietnam.

      Volume: 35 Pages: 91-105

    • Related Report
      2010 Annual Research Report 2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Artin-Schreier DGA and the F_p-fundamental group ofan F_p-scheme2010

    • Author(s)
      Terasoma, T.
    • Journal Title

      Proceedings of the international Colloquium on Cycles, Motives and

      Pages: 493-530

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Thomae type formula for K3 surfaces given by double covers of the projective plane branching along six lines

    • Author(s)
      MATSUMOTO K.-TERASOMA T.
    • Journal Title

      Reine und Angwandte Mathematik

    • Related Report
      2010 Final Research Report
  • [Presentation] Beilinson conjecture for Kuga fiber spaces and relative bar complex2011

    • Author(s)
      Terasoma, T.
    • Organizer
      Arithmetic and Algebraic Geometry 2011
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Year and Date
      2011-01-19
    • Related Report
      2010 Annual Research Report 2009 Annual Research Report
  • [Presentation] Beilinson conjecture for Kuga fiber spaces and relation of mixed elliptic Hopf algebra2010

    • Author(s)
      Terasoma, T.
    • Organizer
      International workshop on motives in Tokyo part6
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Year and Date
      2010-12-13
    • Related Report
      2010 Annual Research Report 2009 Annual Research Report
  • [Presentation] Relative completion and Beilinson conjecture for Kuga fiber sapce, Seoul-Tokyo Conference on Arithmetic and Algebraic Geometry2010

    • Organizer
      KIAS
    • Place of Presentation
      Seul, Korea
    • Year and Date
      2010-11-27
    • Related Report
      2010 Final Research Report
  • [Presentation] Relative completion and Beilinson conjecture for Kuga fiber sapce2010

    • Author(s)
      Terasoma, T.
    • Organizer
      Seoul-Tokyo Conference on Arithmetic and Algebraic Geometry
    • Place of Presentation
      韓国高等科学研究所KIAS(韓国)
    • Year and Date
      2010-11-27
    • Related Report
      2010 Annual Research Report 2009 Annual Research Report
  • [Presentation] 相対高次単数基準とアイゼンシュタイン級数2010

    • Author(s)
      寺杣友秀
    • Organizer
      玉原特殊多様体研究集会
    • Place of Presentation
      玉原国際セミナーハウス
    • Year and Date
      2010-09-07
    • Related Report
      2010 Annual Research Report 2009 Annual Research Report
  • [Presentation] Relative DGA, associated DG category and mixed elliptic motif2010

    • Author(s)
      Terasoma, T.
    • Organizer
      Motives and Homotopy Thory of Schemes
    • Place of Presentation
      オーベルフォルファッハ(ドイツ)
    • Year and Date
      2010-05-20
    • Related Report
      2010 Annual Research Report 2009 Annual Research Report
  • [Presentation] Relative DGA, associated DG category and mixed elliptic motif2010

    • Organizer
      Motives and Homotopy Thory of Schemes
    • Place of Presentation
      Oberwolfach, Germany
    • Related Report
      2010 Final Research Report
  • [Presentation] Bar complex and Tannakian category2009

    • Organizer
      seminaire de theorie des nobres
    • Place of Presentation
      Jussieu, Paris
    • Year and Date
      2009-10-19
    • Related Report
      2010 Final Research Report
  • [Presentation] Motivic construction of relative completion2009

    • Organizer
      1st PRIMA Congress
    • Place of Presentation
      Sydney
    • Year and Date
      2009-07-06
    • Related Report
      2010 Final Research Report
  • [Presentation] Thomae's formula for triple covering and binary trees2009

    • Author(s)
      寺杣友秀
    • Organizer
      International conference on Complex Geometry
    • Place of Presentation
      Hanoi University of Education, ベトナム
    • Year and Date
      2009-01-15
    • Related Report
      2008 Annual Research Report
  • [Presentation] DG category, Bar complex and their applications2009

    • Organizer
      Cycles, Motives and Shimura Varieties
    • Place of Presentation
      Tata Institute Mumbai
    • Year and Date
      2009-01-07
    • Related Report
      2010 Final Research Report
  • [Presentation] Thomae's formula の公式に現れる定数と binary graph2008

    • Author(s)
      寺杣友秀
    • Organizer
      ワークショップ「テータ関数と可積分分系」
    • Place of Presentation
      九州大学
    • Year and Date
      2008-12-21
    • Related Report
      2008 Annual Research Report
  • [Presentation] Thomae's formula and binary tree2008

    • Organizer
      城崎代数幾何シンポジウム
    • Year and Date
      2008-10-21
    • Related Report
      2010 Final Research Report
  • [Presentation] Thomae's formula and binary tree2008

    • Author(s)
      寺杣友秀
    • Organizer
      城崎代数幾何シンポジウム
    • Place of Presentation
      兵庫県城崎大会議場
    • Year and Date
      2008-10-21
    • Related Report
      2008 Annual Research Report
  • [Presentation] Artin-Schreier DGAとFp unit root cristal2008

    • Author(s)
      寺杣友秀
    • Organizer
      東北大学談話会
    • Place of Presentation
      東北大学
    • Year and Date
      2008-10-06
    • Related Report
      2008 Annual Research Report
  • [Presentation] Thomae's formula for triple covering and binary trees2008

    • Organizer
      International conference on Complex Geometry
    • Place of Presentation
      Hanoi University of Education
    • Year and Date
      2008-01-15
    • Related Report
      2010 Final Research Report
  • [Remarks] ホームページ等

    • URL

      http://gauss.ms.u-tokyo.ac.jp

    • Related Report
      2010 Final Research Report
  • [Remarks]

    • URL

      http://gauss.ms.u-tokyo.ac.jp

    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://gauss.ms.u-tokyo.ac.jp

    • Related Report
      2009 Annual Research Report

URL: 

Published: 2008-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi