Research on foundations of p-adic Hodge theory and their application

• Project/Area Number: 18540015
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: The University of Tokyo
• Principal Investigator: TSUJI Takeshi The University of Tokyo, 大学院・数理科学研究科, 准教授 (40252530)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,640,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥540,000); Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2007: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2006: ¥1,300,000 (Direct Cost: ¥1,300,000)
• Keywords: p進Hodge 理論 / D 加群 / ポリログ層 / P進Hodge理論 / 数論的D加群 / フユージョン則 / p進Hodge理論 / p進L関数 / semi-stable層

Research Abstract

p 進エタール局所系に対する基礎概念Hodge-Tate, de Rham, crystalline が, 特殊ファイバーの生成点での様子だけで決定されることを明らかにした. また p 進体上の半安定還元をもつ代数多様体のべき単基本群のp 進Hodge 理論に対し, p 進エタール局所系のp 進Hodge 理論の観点からの解釈を与えた. その他, 数論的D 加群を用いた新しい視点からのlog crystallinecohomology の研究, 虚数乗法をもつ楕円曲線のp 進楕円ポリログ層の構造の完全な決定を行った.

Research Products

• [Presentation] Nearby cycles and D-modules of logschemes in characteristic p>0 (2008)
  • Author(s): 辻雄
  • Organizer: P-adicmethod and its applications in arithmeticgeometry at Sendai
  • Place of Presentation: 東北大学
  • Year and Date: 2008-11-07
• [Presentation] Nearby cycles and D-modules of logschemes in characteristic p>0 (2008)
  • Author(s): 辻雄
  • Organizer: RecentProgress in Arithmetic D-modules theory
  • Place of Presentation: IRMA, Universite deStrasbourg
  • Year and Date: 2008-10-03
• [Presentation] On purity for p-adicrepresentations (2008)
  • Author(s): 辻雄
  • Organizer: Workshop : ArithmeticApplications of p-adic Analysis and RigidSpaces
  • Place of Presentation: Universitat Regensburg
  • Year and Date: 2008-02-22
• [Presentation] On purity for p-adic representations (2008)
  • Author(s): 辻 雄
  • Organizer: Arithmetic applications of p-adic analysis and rigid spaces
  • Place of Presentation: レーゲンスブルグ大学
  • Year and Date: 2008-02-22
• [Presentation] On purity for p-adicrepresentations (2007)
  • Author(s): 辻雄
  • Organizer: Of ramification andVanishing Cycles
  • Place of Presentation: 東京大学
  • Year and Date: 2007-09-11
• [Presentation] On purity for p-adic representations (2007)
  • Author(s): 辻 雄
  • Organizer: Of ramification and vanishing cycles
  • Place of Presentation: 東京大学
  • Year and Date: 2007-09-11
• [Presentation] On purity for p-adicrepresentations (2007)
  • Author(s): 辻雄
  • Organizer: p-adic method and itsapplications in arithmetic geometry 2007
  • Place of Presentation: 東京大学
  • Year and Date: 2007-06-11
• [Presentation] On purity for p-adic representations (2007)
  • Author(s): 辻 雄
  • Organizer: p-adic method and its applications in arithmetic geometry 2007
  • Place of Presentation: 東京大学
  • Year and Date: 2007-06-11
• [Presentation] On log crystalline cohomology andarithmetic D-modules (2006)
  • Author(s): 辻雄
  • Organizer: Workshop : p-adicArithmetic Geometry
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2006-11-22
• [Presentation] On semi-stable smooth p-adic etalesheaves (2006)
  • Author(s): 辻雄
  • Organizer: Workshop : Arithmetic AlgebraicGeometry
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2006-09-12
• [Presentation] On semi-stable smooth p-adicsheaves (2006)
  • Author(s): 辻雄
  • Organizer: International conference : Hodgetheory
  • Place of Presentation: San Servolo,Venice, Italy
  • Year and Date: 2006-06-24