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

报告人: Dr. Heng DU (YMSC)

时间: 2022年12月15日 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 Fontaine’s 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.