Abstract Hui Gao

Hui Gao will speak on

Locally analytic vectors and overconvergent $(\varphi, \tau)$-module

Abstract: In $p$-adic Hodge theory, we use various ``linear algebra" objects to study $p$-adic Galois representations of $G_K$ (where $K$ is for example a finite extension of $\mathbb{Q}_p$, and $G_K$ the Galois group). In this talk, we discuss the so-called $(\varphi, \tau)$-modules which are constructed by Caruso; they are analogues of the more well-known $(\varphi, \Gamma)$-modules, and they also classify $p$-adic Galois representations. We will study locally analytic vectors in some period rings and in the $(\varphi, \tau)$-modules; this enables us to establish the overconvergence property of the $(\varphi, \tau)$-modules. This is joint work with L\'eo Poyeton.