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 with -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.
|Overview, Goal and Motivation.
|Cyclotomic Characters, -adic and p-adic Galois representations attached to elliptic curves.
|Properties of and Ax-Sen-Tate theorem.
|Hodge-Tate representations and the decomposition theorem.
|NO TALK (due to YRANT 2019)
|Formalism of period rings and .
|and de Rham representations.
|, Crystalline representations, examples from elliptic curves.
|Bringing it all back home