D-modules over a p-adic field and p-adic Hodge theory

• Project/Area Number: 24540009
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: The University of Tokyo
• Principal Investigator: TSUJI Takeshi 東京大学, 数理(科)学研究科(研究院), 教授 (40252530)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000); Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: p-adic Hodge theory / perverse sheaf / D-module / Higgs bundle / Simpson correspondence / perverse層 / D加群 / Higgs束 / p進Simpson対応 / p進Hodge理論 / 整数論 / 数論幾何学 / 代数学

Outline of Final Research Achievements

We studied p-adic Hodge theory for p-adic perverse sheaves and p-adic Simpson correspondence. For the former, we gave descriptions of cohomologies of p-adic perverse sheaves, with the stratification along a simple normal crossing divisor, and corresponding arithmetic D-modules in terms of the gluing data on the strata, which allow us to construct a comparison map with the two cohomologies. For the latter, we established a cohomology theory for Higgs isocrystals and also gave a proof of the equivalence of categories in the local p-adic Simpson correspondence.

Research Products

• [Presentation] On p-adic etale cohomology of perverse sheaves (2014)
  • Author(s): Takeshi Tsuji
  • Organizer: Pan Asian Number Theory 2014, POSTECH, Korea
  • Place of Presentation: POSTECH, Korea
  • Year and Date: 2014-08-05 – 2014-08-09
  • Invited
• [Presentation] The p-adic Simpson correspondence and Higgs isocrystals (2013)
  • Author(s): 辻雄
  • Organizer: Conference Theorie de Hodge p-adique et Developpements
  • Place of Presentation: Institut des Hautes Etudes Scientifiques, IHES
  • Invited
• [Presentation] p-adic perverse sheaves and arithmetic D-modules with singularities along a simple normal crossing divisor (2012)
  • Author(s): 辻雄
  • Organizer: Arithmetic Geometry week in Tokyo
  • Place of Presentation: 東京大学
  • Invited
• [Presentation] p-adic perverse sheaves and arithmetic D- modules with singularities along a simple normal crossing divisor (2012)
  • Author(s): 辻雄
  • Organizer: Algebraic K-theory and Arithmetic,
  • Place of Presentation: Banach Center, Bedlewo, ポーランド
  • Invited
• [Presentation] Higgs crystals (2012)
  • Author(s): 辻雄
  • Organizer: Summer School: Higgs bundles on p-adic curves and representation theory
  • Place of Presentation: The University of Mainz, ドイツ
  • Invited
• [Presentation] The p-adic Simpson correspondence and Higgs crystals (2012)
  • Author(s): 辻雄
  • Organizer: p-adic cohomology and its applications to arithmetic geometry
  • Place of Presentation: 東北大学
  • Invited