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

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Speaker:
Hui Gao
Affiliation:
University of Helsinki
Date:
Wed, 2018-10-10 14:30 - 15:30
Location:
MPIM Lecture Hall
Parent event:
Number theory lunch seminar

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 $(\varphi, \tau)$-module; this enables us to establish the overconvergence property of the $(\varphi, \tau)$-modules. This is joint work with L\'eo Poyeton.

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