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#### Seminar der Forschergruppe 'Symmetrie, Geometrie und Arithmetik'

„Locally analytic vectors and overconvergent (phi, tau)-module“
Dr. Hui Gao, University of Helsinki

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.

Freitag, den 19. Oktober 2018 um 13:30 Uhr, in INF 205, SR A Freitag, den 19. Oktober 2018 at 13:30, in INF 205, SR A