Abstract:

Let $K$ be a $p$-adic local field and let $G_K$ denote the absolute Galois group of $K$. The aim of $p$-adic Hodge theory is to extract information of $p$-adic representations of $G_K$, in particular of those from geometry. The goal of this mini-course is to introduce some of the objects and techniques which are used to study $p$-adic representations. 
More precisely, at first, we plan to introduce the definitions and basic properties of Hodge-Tate, de Rham, crystalline and semi-stable representations and their relations to geometry. Then we will study the theory of $(\varphi,\Gamma)$-modules, and if time permits, also study the overconvergent version and their cohomology theory.

Reference:

O. Brinon, B. Conrad, CMI Summer Notes on $p$-adic Hodge Theory, 2009.
S. Hong. Notes on $p$-adic Hodge Theory, 2020.

Time:

10/20、10/21、10/27、10/28、11/3、11/4    10:00-11:30