学术报告

12-12-2022

A sheaf theoretic approach to overconvergence of \’etale (\phi, \Gamma)-modules.

Title: A sheaf theoretic approach to overconvergence of \etale (\phi, \Gamma)-modules.

报告人: Dr. Heng DU (YMSC)

时间: 20221215 14:00-15:00

腾讯会议: 564-129-924

Abstract: The theory of (\phi, \Gamma)-modules introduced by Fontaine describes Q_p-valued continuous representations of the absolute Galois group of a p-adic field in terms of semi-linear algebra objects. There is a refinement of Fontaines result by Cherbonnier and Colmez that replace the Cohen rings used by Fontaine with smaller rings consisting of so-called convergent elements. Recently there has been a sheaf theoretic approach to the theory of (\phi, \Gamma)-modules by Bhatt and Scholze using prismatic Laurent F-crystals. In this talk, we will prove the analog result of Cherbonnier and Colmez in the content of Bhatt and Scholze. This will lead to new results of the overconvergence of \Phi-iterate towers. This is based on joint work with Tong Liu.

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