Geometry and arithmetic of period integrals and motives

• Project/Area Number: 23340001
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: The 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: ¥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.

Research Products

• [Journal Article] On p-adic differential equation on semi-stabke variety II (2015)
  • 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
  • Peer Reviewed
• [Journal Article] Monodromy of Lauricella's hypergeometric FA-system (2014)
  • Author(s): Matsumoto Keiji and Yoshida Masaaki
  • Journal Title: Ann. Sc. Norm. Super. Pisa Cl. Sci Volume: 13-2 Pages: 551-577
  • Peer Reviewed
• [Journal Article] All order alpha prime expansion of superstring tree from the Drinfeld associator (2014)
  • 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
  • Peer Reviewed
• [Journal Article] Monodromy and Pfaffian of Lauricella`s FD in terms of the intersection forms of twisted (co)homology of groups (2013)
  • Author(s): Ｋ．Ｍａｔｓｕｍｏｔｏ
  • Journal Title: Kyushu Journal of Mathematics Volume: 67 Pages: 367-387
  • Peer Reviewed
• [Journal Article] The Hodge realization of Tate motives (2013)
  • Author(s): Kenichiro Kimura
  • Journal Title: 数理解析研究所講究録 Volume: 1840 Pages: 139-148
  • 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
  • Peer Reviewed
• [Journal Article] Cut-by-curves criterion for the log extendability of overconvergent isocrystals (2012)
  • Author(s): Shiho, Atsushi
  • Journal Title: Math.Z. Volume: 269-1,2 Pages: 59-82
  • Peer Reviewed
• [Journal Article] Limits of interations of complex maps and hypergeometric functions (2011)
  • Author(s): Matsumot, K.-Oikawa, T.
  • Journal Title: Hokkaido mathematical Journal Volume: 41 Pages: 135-155
  • Peer Reviewed
• [Journal Article] Theomae type formula for K3 surfaces given by doubole covering fo the projective plane brancehing along six lines (2011)
  • 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
  • Peer Reviewed
• [Journal Article] Purity for overconvergence (2011)
  • Author(s): Shiho, A.
  • Journal Title: Selecta Math Volume: 17 Pages: 833-854
  • 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
  • Peer Reviewed
• [Presentation] Period map of mixed Hodge structures for certain triple coverings (2015)
  • Author(s): Tomohide Terasoma
  • Organizer: Curves, Moduli and Integrable systems
  • Place of Presentation: 津田塾大学
  • Year and Date: 2015-02-17
  • Invited
• [Presentation] Mixed elliptic motives and depth filtration of multiple zeta values (2015)
  • 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
  • Invited
• [Presentation] Depth filitration and mixed elliptic motives (2014)
  • 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
  • Invited
• [Presentation] Depth flitration of multiple zeta values and Tate curves (2014)
  • Author(s): Tomohide Terasoma
  • Organizer: Conference on Hodge Theoryand L2-cohomology
  • Place of Presentation: Johns Hopkins University
  • Year and Date: 2014-11-22
  • Invited
• [Presentation] A flitration arising from representation of Tate curves (2014)
  • Author(s): Tomohide Terasoma
  • Organizer: Workshops on multiple zeta values
  • Place of Presentation: 九州大学
  • Year and Date: 2014-08-23
  • Invited
• [Presentation] A construction of surfaces with non-trivial Higher Chow groups (2014)
  • Author(s): T. Terasoma
  • Organizer: Arithmetic and Algebraic Geometry
  • Place of Presentation: 東京大学数理科学研究科
  • Invited
• [Presentation] On differential Artin conductor of overconvergent iscocrystals (2014)
  • 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
  • Invited
• [Presentation] On homotopy exact sequence for log de Rham fundamental groups (2014)
  • Author(s): 志甫淳
  • Organizer: p-adic cohomology and its applications 2014
  • Place of Presentation: 東北大学
  • Invited
• [Presentation] Ｃｏｈｏｍｏｌｏｇｉｃａｌ ｒｅｐｒｅｓｅｎｔａｔｉｏｎ ｏｆ Ｇｒｏｔｈｅｎｄｉｅｃｋ Ｔｅｉｃｈｍｕｌｌｅｒ ｇｒｏｕｐ (2013)
  • Author(s): T. Terasoma
  • Organizer: Ｒｅｃｅｎｔ ａｄｖａｎｃｅｓ ｉｎ Ｈｏｄｇｅ Ｔｈｅｏｒｙ； Ｐｅｒｉｏｄ Ｄｏｍａｉｎｓ， Ａｌｇｅｂｒａｉｃ ｃｙｃｌｅｓ， ａｎｄ Ａｒｉｔｈｍｅｔｉｃ
  • Place of Presentation: ＵＢＣ， Ｖａｎｃｏｕｖｅｒ
  • 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
  • Invited
• [Presentation] Hyergeometric identitiesand Brown=Zagier identities (2013)
  • 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
  • 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
  • Invited
• [Presentation] Chow cohomology group of singular algebraic surfaces (2013)
  • 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
  • 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
  • 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
  • Invited
• [Presentation] On restriction of overconvergent isocrystals (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
  • Invited
• [Presentation] On a generalization of local Ogus-Vologodsky correspondence (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
  • Invited
• [Presentation] Chow cohomology group of singular algebraic surfaces (2013)
  • 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
  • Invited
• [Presentation] Deligne bar complexに関するcomparizon copath (2012)
  • 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
• [Presentation] Hodge realization of mixed Tate motives via period integral (2012)
  • 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
• [Presentation] Motif associated to fundamental group of universal elliptic curvesand its regulator (2012)
  • 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
• [Presentation] Bar comodles associated to fundamental group of punctured elliptic curves (2011)
  • 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
• [Presentation] On extension and restriction of overconvergent isocristals (2011)
  • 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
• [Presentation] On extension and restriction overconvergent isocristals (2011)
  • 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
• [Presentation] Relative regulator and automorphic L-functions (2011)
  • 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
• [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
• [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
• [Presentation] Hodge realization of mixed Tate motives (2011)
  • 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
• [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
• [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
• [Presentation] Relative regulator for Kuga fiberspace and Beilinson conjecture (2011)
  • 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