Hodge-Tate Study Group

The aim of this study group is to give an introduction to the theory of p-adic Galois representations, that is, representations of the absolute Galois group of $\mathbb{Q}_p$ with $p$ -adic coefficients. We will see how they arise from the (global) Galois representations attached to elliptic curves, and study the categories of Hodge-Tate, de Rham and crystalline Galois representations and the relationships between them.

The main reference is "" by Laurent Berger.

We will follow also "" by Olivier Brinon and Brian Conrad.

Finally, it could be useful also refer to Abhinandan's master thesis "".

We would like to present the theory throughout the following schedule.

Date	Title	Speaker
11/10/2019	Overview, Goal and Motivation.	Chris Lazda
18/10/2019	Cyclotomic Characters, $\ell$ -adic and p-adic Galois representations attached to elliptic curves.	Mattia Sanna
25/10/2019	Properties of $\mathbb{C}_p$ and Ax-Sen-Tate theorem.	Zeping Hao
1/11/2019	Hodge-Tate representations and the decomposition theorem.	Steven Groen
8/11/2019	NO TALK (due to YRANT 2019)	--
15/11/2019	Formalism of period rings and $B_{HT}$ .	Philippe Michaud-Rogers
22/11/2019	$B_{dR}$ and de Rham representations.	Chris Williams
29/11/2019	$B_{cris}$ , Crystalline representations, examples from elliptic curves.	Rob Rockwood
6/12/2019	Bringing it all back home	TBA

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Hodge-Tate Study Group