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

2014 Fiscal Year Final Research Report

• 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
• Keywords: p-adic Hodge theory / perverse sheaf / D-module / Higgs bundle / Simpson correspondence

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.

Free Research Field

数論幾何学