p-adic Hodge Theory and Anabelian Geometry
Project/Area Number |
17H06782
|
Research Category |
Grant-in-Aid for Research Activity Start-up
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Allocation Type | Single-year Grants |
Research Field |
Algebra
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Research Institution | Kyoto University |
Principal Investigator |
Tan Fucheng 京都大学, 数理解析研究所, 講師 (00803587)
|
Project Period (FY) |
2017-08-25 – 2019-03-31
|
Project Status |
Completed (Fiscal Year 2018)
|
Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
|
Keywords | p-adic Hodge理論 / p-adic Hodge theory / Simpson correspondence / JSPSH30 / crystalline comparison |
Outline of Final Research Achievements |
During the research period, I have been working on the crystalline comparison theorem in p-adic Hodge theory for the more general semi-stable comparison problem, with non-trivial coefficients and in the relative setting. Now I am able to formulate integral results for etale and crystalline cohomology with non-trivial coefficients. The relative version of such results shall need further investigation. Meanwhile, due to the advances above, I was able to spend a considerably large amount of time on Simpson correspondence. At the current stage, my focus is mainly on hyperbolic curves of low genus. Currently, it is clear to me that to formulate an arithmetic version of Simpson correspondence, one needs to start from the theory of Ogus-Vologodski in characteristic p. This allows us to glue the various p-adic Galois representation and Higgs modules at almost all places of a number field. This shares the similarity with the modularity conjectures such as that of Fontaine-Mazur.
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Academic Significance and Societal Importance of the Research Achievements |
私の研究プロジェクトは、p進ホッジ理論の主なテーマを明確にすること、そしてそれを他の数学研究の分野に適用することを目指しています。 私の研究は日本がこの中央研究分野での役割を維持するのを助けています。 そして、数学の社会が生きるために必要かつ重要であるこのトピックを学生が学ぶことも可能にしました。
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Report
(3 results)
Research Products
(4 results)