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 "An introduction to the theory of p-adic representations" by Laurent Berger.

We will follow also "CMI Summer School Notes on p-Adic Hodge Theory" by Olivier Brinon and Brian Conrad.

Finally, it could be useful also refer to Abhinandan's master thesis "p-adic Galois representations and Elliptic Curves".

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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