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# Master seminar p-adic Galois representations

**Program**: Seminar program p-adic Galois representations

**Date & time:** Tuesday 14-16

**First session:** November 3, 2020

**Place:** online via Zoom (see moodle)

**Moodle:** There is an electronic classroom for the seminar on the moodle platform. Read backward, the enrolment key needed to subscribe is

12/02snoitatneserpeRsiolaGcida-p

**Prerequisites:** You need a strong background in algebra and some general structure theory of nonarchimedean fields. For a few talks some basic knowledge of algebraic geometry might be helpful

**Requirements:** According to the regulations of our master program each participant is supposed to give two talks.

**Content:** One of the main objectives of algebraic number theory is to understand the absolute Galois group of a local or a global field. We will focus on nonarchimedean local fields of residue characteristic p and study their absolute Galois groups through so-called p-adic representations, i.e. continuous linear actions on finite dimensional p-adic vector spaces. In this setting, large parts of the theory go back to Jean-Marc Fontaine and his school.

The topics covered include examples from algebraic geometry, étale phi-modules, the tilting equivalence for perfectoid fields, étale (phi,Gamma)-modules, the formalism of period rings, Hodge-Tate representations, de Rham representations, crystalline representations, semistable representations, filtered isocrystals and the main theorems of p-adic Hodge theory.

**Registration:** If you wish to give a talk please enrol in the electronic class room and send me an email. Please indicate possible preferences concerning the talks. The final schedule will be published on moodle in September.