Published on *Max Planck Institute for Mathematics* (https://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Hui Gao
Affiliation:

University of Helsinki
Date:

Wed, 2018-10-10 14:30 - 15:30 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.

**Links:**

[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] https://www.mpim-bonn.mpg.de/node/3444

[3] https://www.mpim-bonn.mpg.de/node/246