Study on overconvergent isocrystals

2016 Fiscal Year Final Research Report

• Project/Area Number: 25400008
• 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: Shiho Atsushi 東京大学, 大学院数理科学研究科, 教授 (30292204)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: アイソクリスタル / エタール基本群 / ドラーム基本群 / 対数的代数多様体 / p進微分方程式

Outline of Final Research Achievements

We checked the compatibility of the algebraization functor from the category of log overconvergent isocrystals to that of modules with integrable connection with the formation of tensor products under certain assumption. We proved a partial generalization of Ogus-Vologodsky correspondence on schemes in which p is nilpotent. We proved under certain assumption a conjecture of de Jong on isocrystals on algebraic varieties with trivial etale fundamental group. We constructed in purely algebraic way the homotopy exact sequence (including the first injection) for certain quotient of de Rham fundamental groups of certain log algebraic varieties. We studied in purely algebraic way the relative pro-unipotent de Rham fundamental groups for certain morphisms of log algebraic varieties, and gave a p-adic application of it. We studied to fix errors in the proof of fundamental theorems in the theory of p-adic differential equations.

Free Research Field

数論幾何学