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Geometry and arithmetic of period integrals and motives

Research Project

Project/Area Number 23340001
Research Category

Grant-in-Aid for Scientific Research (B)

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

Principal Investigator

TERASOMA Tomohide  東京大学, 数理(科)学研究科(研究院), 教授 (50192654)

Co-Investigator(Kenkyū-buntansha) HANAMURA Masaki (SHIHO Atsushi / MATSUMOTO Keiji / KIMURA Kenichirou)  東北大学, 理学研究科, 教授 (60189587)
松本 圭司  北海道大学, 理学(系)研究科(研究院), 教授 (30229546)
志甫 淳  東京大学, 数理(科)学研究科(研究院), 教授 (30292204)
木村 健一郎  筑波大学, 数理物質科学研究科(系), 講師 (50292496)
Project Period (FY) 2011-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥12,740,000 (Direct Cost: ¥9,800,000、Indirect Cost: ¥2,940,000)
Fiscal Year 2014: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2013: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2012: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2011: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Keywordsモチーフ / 周期積分 / 代数的サイクル / コホモロジー / 周期写像 / ホッジ理論 / 算術幾何 / テータ関数 / モジュラー多様体
Outline of Final Research Achievements

We construct a complex using semi-algebraic set and prove generalized Cauchy formula to construct a Hodge realization functor of mixed Tate motives.
We introduce a motivic filtration which gives a depth filtration. We construct surfaces which have big images of cycle maps from higher Chow groups to cohomologies.
We study Schwarz maps for reducible hypergeometric systems of two variable with a special parameter. We describe the inverse period map using theta function. We give a description of the image of Abel-Jacobi map corresponding to a family of genus two curves.

Report

(5 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Annual Research Report
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • Research Products

    (42 results)

All 2015 2014 2013 2012 2011

All Journal Article (11 results) (of which Peer Reviewed: 11 results) Presentation (31 results) (of which Invited: 18 results)

  • [Journal Article] On p-adic differential equation on semi-stabke variety II2015

    • Author(s)
      DiProietto, Valentina, Shiho,Atsushi
    • Journal Title

      Manuscripta Mathematica

      Volume: 146 Issue: 1-2 Pages: 179-199

    • DOI

      10.1007/s00229-014-0691-9

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Monodromy of Lauricella's hypergeometric FA-system2014

    • Author(s)
      Matsumoto Keiji and Yoshida Masaaki
    • Journal Title

      Ann. Sc. Norm. Super. Pisa Cl. Sci

      Volume: 13-2 Pages: 551-577

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] All order alpha prime expansion of superstring tree from the Drinfeld associator2014

    • Author(s)
      J.Broedel, O.Schlotterer, S.Stieberger, T.Terasoma
    • Journal Title

      Phycal Review D

      Volume: D89 Issue: 6

    • DOI

      10.1103/physrevd.89.066014

    • Related Report
      2013 Annual Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Monodromy and Pfaffian of Lauricella`s FD in terms of the intersection forms of twisted (co)homology of groups2013

    • Author(s)
      K.Matsumoto
    • Journal Title

      Kyushu Journal of Mathematics

      Volume: 67 Pages: 367-387

    • Related Report
      2013 Annual Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Hodge realization of Tate motives2013

    • Author(s)
      Kenichiro Kimura
    • Journal Title

      数理解析研究所講究録

      Volume: 1840 Pages: 139-148

    • Related Report
      2013 Annual Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 相対的な代数的対応と混合モティーフ層2013

    • Author(s)
      Masaki Hanamura
    • Journal Title

      数理研講究録別冊

      Volume: B44 Pages: 85-98

    • Related Report
      2013 Annual Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Cut-by-curves criterion for the log extendability of overconvergent isocrystals2012

    • Author(s)
      Shiho, Atsushi
    • Journal Title

      Math.Z.

      Volume: 269-1,2 Pages: 59-82

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Limits of interations of complex maps and hypergeometric functions2011

    • Author(s)
      Matsumot, K.-Oikawa, T.
    • Journal Title

      Hokkaido mathematical Journal

      Volume: 41 Pages: 135-155

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Theomae type formula for K3 surfaces given by doubole covering fo the projective plane brancehing along six lines2011

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

      Journal fur die reine und angewandte Mathematik

      Volume: 114 Issue: 665

    • DOI

      10.1515/crelle.2011.114

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Purity for overconvergence2011

    • Author(s)
      Shiho, A.
    • Journal Title

      Selecta Math

      Volume: 17 Pages: 833-854

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] P進微分方程式と過収束アイソクリスタル2011

    • Author(s)
      志甫淳
    • Journal Title

      数学

      Volume: 63-4 Pages: 369-395

    • NAID

      130004558952

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Presentation] Period map of mixed Hodge structures for certain triple coverings2015

    • Author(s)
      Tomohide Terasoma
    • Organizer
      Curves, Moduli and Integrable systems
    • Place of Presentation
      津田塾大学
    • Year and Date
      2015-02-17
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Mixed elliptic motives and depth filtration of multiple zeta values2015

    • Author(s)
      Tomohide Terasoma
    • Organizer
      Arithmetic and Algebraic Geometry 2015
    • Place of Presentation
      東京大学数理科学研究科
    • Year and Date
      2015-01-27
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Depth filitration and mixed elliptic motives2014

    • Author(s)
      Tomohide Terasoma
    • Organizer
      Workshop on Multiple Zeta Values, Modular Forms and Elliptic
    • Place of Presentation
      ICMAT, Madrid
    • Year and Date
      2014-12-03
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Depth flitration of multiple zeta values and Tate curves2014

    • Author(s)
      Tomohide Terasoma
    • Organizer
      Conference on Hodge Theoryand L2-cohomology
    • Place of Presentation
      Johns Hopkins University
    • Year and Date
      2014-11-22
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] A flitration arising from representation of Tate curves2014

    • Author(s)
      Tomohide Terasoma
    • Organizer
      Workshops on multiple zeta values
    • Place of Presentation
      九州大学
    • Year and Date
      2014-08-23
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] A construction of surfaces with non-trivial Higher Chow groups2014

    • Author(s)
      T. Terasoma
    • Organizer
      Arithmetic and Algebraic Geometry
    • Place of Presentation
      東京大学数理科学研究科
    • Related Report
      2013 Annual Research Report 2012 Annual Research Report
    • Invited
  • [Presentation] On differential Artin conductor of overconvergent iscocrystals2014

    • Author(s)
      志甫淳
    • Organizer
      Arithmetic and Algebraic Geometry 2014
    • Place of Presentation
      東京大学数理科学研究科
    • Related Report
      2013 Annual Research Report 2012 Annual Research Report
    • Invited
  • [Presentation] On homotopy exact sequence for log de Rham fundamental groups2014

    • Author(s)
      志甫淳
    • Organizer
      p-adic cohomology and its applications 2014
    • Place of Presentation
      東北大学
    • Related Report
      2013 Annual Research Report 2012 Annual Research Report
    • Invited
  • [Presentation] Cohomological representation of Grothendieck Teichmuller group2013

    • Author(s)
      T. Terasoma
    • Organizer
      Recent advances in Hodge Theory; Period Domains, Algebraic cycles, and Arithmetic
    • Place of Presentation
      UBC, Vancouver
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Grothendieck Teichmuller群のコホモロジー的表現2013

    • Author(s)
      寺杣 友秀
    • Organizer
      大阪大学談話会
    • Place of Presentation
      大阪大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Hyergeometric identitiesand Brown=Zagier identities2013

    • Author(s)
      寺杣 友秀
    • Organizer
      多重ゼータ値の諸相
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 不完全周期積分の逆周期写像について2013

    • Author(s)
      松本 圭司
    • Organizer
      玉原特殊多様体研究集会
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Related Report
      2013 Annual Research Report 2012 Annual Research Report
    • Invited
  • [Presentation] Chow cohomology group of singular algebraic surfaces2013

    • Author(s)
      花村昌樹
    • Organizer
      特殊多様体研究集会
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] p進微分方程式と係数つきリジッドコホモロジー2013

    • Author(s)
      志甫淳
    • Organizer
      大阪大学談話会
    • Place of Presentation
      大阪大学
    • Related Report
      2013 Annual Research Report 2012 Annual Research Report
    • Invited
  • [Presentation] p進数とp進微分方程式2013

    • Author(s)
      志甫淳
    • Organizer
      豊田中央研数学コロキウム
    • Place of Presentation
      豊田中央研究所
    • Related Report
      2013 Annual Research Report 2012 Annual Research Report
    • Invited
  • [Presentation] On restriction of overconvergent isocrystals2013

    • Author(s)
      志甫淳
    • Organizer
      豊田中央研数学コロキウム
    • Place of Presentation
      豊田中央研究所
    • Related Report
      2013 Annual Research Report 2012 Annual Research Report
    • Invited
  • [Presentation] On a generalization of local Ogus-Vologodsky correspondence2013

    • Author(s)
      志甫淳
    • Organizer
      豊田中央研数学コロキウム
    • Place of Presentation
      豊田中央研究所
    • Related Report
      2013 Annual Research Report 2012 Annual Research Report
    • Invited
  • [Presentation] Chow cohomology group of singular algebraic surfaces2013

    • Author(s)
      花村昌樹
    • Organizer
      玉原特殊多様体研究集会
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Deligne bar complexに関するcomparizon copath2012

    • Author(s)
      寺杣友秀
    • Organizer
      代数幾何とモチーフ理論ワークショップ
    • Place of Presentation
      東北大学(招待講演)
    • Year and Date
      2012-03-09
    • Related Report
      2011 Annual Research Report
  • [Presentation] Hodge realization of mixed Tate motives via period integral2012

    • Author(s)
      木村健一郎
    • Organizer
      代数幾何とモチーフ理論ワークショップ
    • Place of Presentation
      東北大学(招待講演)
    • Year and Date
      2012-03-08
    • Related Report
      2011 Annual Research Report
  • [Presentation] Motif associated to fundamental group of universal elliptic curvesand its regulator2012

    • Author(s)
      寺杣友秀
    • Organizer
      Arithmetic and algebraic geometry 2012
    • Place of Presentation
      東京大学
    • Year and Date
      2012-02-17
    • Related Report
      2011 Annual Research Report
  • [Presentation] Bar comodles associated to fundamental group of punctured elliptic curves2011

    • Author(s)
      寺杣友秀
    • Organizer
      Taiwan-Japan workshop on Arithmetic Algebraic Geometry and Related topics
    • Place of Presentation
      Academia Sinica, Taiwan(招待講演)
    • Year and Date
      2011-11-19
    • Related Report
      2011 Annual Research Report
  • [Presentation] On extension and restriction of overconvergent isocristals2011

    • Author(s)
      志甫淳
    • Organizer
      Japan Taisan workshop on Ariithmetic Algebraic Geometry and related topics
    • Place of Presentation
      Academia Sinica, Taiwan(招待講演)
    • Year and Date
      2011-11-19
    • Related Report
      2011 Annual Research Report
  • [Presentation] On extension and restriction overconvergent isocristals2011

    • Author(s)
      志甫淳
    • Organizer
      東京パリ数論幾何セミナー
    • Place of Presentation
      東京大学(招待講演)
    • Year and Date
      2011-11-09
    • Related Report
      2011 Annual Research Report
  • [Presentation] Relative regulator and automorphic L-functions2011

    • Author(s)
      寺杣友秀
    • Organizer
      代数幾何シンポジウム
    • Place of Presentation
      城崎大会議場(招待講演)
    • Year and Date
      2011-10-27
    • Related Report
      2011 Annual Research Report
  • [Presentation] 局所Ogus-Vologodsky対応の一般化について2011

    • Author(s)
      志甫淳
    • Organizer
      東北大学談話会
    • Place of Presentation
      東北大学(招待講演)
    • Year and Date
      2011-10-17
    • Related Report
      2011 Annual Research Report
  • [Presentation] 過収束アイソクリスタル2011

    • Author(s)
      志甫淳
    • Organizer
      日本数学会総合講演
    • Place of Presentation
      信州大学(招待講演)
    • Year and Date
      2011-09-29
    • Related Report
      2011 Annual Research Report
  • [Presentation] Hodge realization of mixed Tate motives2011

    • Author(s)
      木村健一郎
    • 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(招待講演)
    • Year and Date
      2011-09-07
    • Related Report
      2011 Annual Research Report
  • [Presentation] P進表現とp進微分方程式:正票数局所体の場合、正票数代数多様体の場合2011

    • Author(s)
      志甫淳
    • Organizer
      仙台シンポジウム
    • Place of Presentation
      東北大学(招待講演)
    • Year and Date
      2011-08-10
    • Related Report
      2011 Annual Research Report
  • [Presentation] P進微分方程式の対数的延長について2011

    • Author(s)
      志甫淳
    • Organizer
      東京大学談話会
    • Place of Presentation
      東京大学(招待講演)
    • Year and Date
      2011-06-04
    • Related Report
      2011 Annual Research Report
  • [Presentation] Relative regulator for Kuga fiberspace and Beilinson conjecture2011

    • Author(s)
      寺杣友秀
    • Organizer
      Workshop on multiple zeta values, modular forms and mixed elliptic motives
    • Place of Presentation
      Bristol University(イギリス)(招待講演)
    • Year and Date
      2011-05-06
    • Related Report
      2011 Annual Research Report

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Published: 2011-04-06   Modified: 2019-07-29  

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