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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