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.
|11/10/2019||Overview, Goal and Motivation.||Chris Lazda|
|18/10/2019||Cyclotomic Characters, -adic and p-adic Galois representations attached to elliptic curves.||Mattia Sanna|
|25/10/2019||Properties of and Ax-Sen-Tate theorem.||Zeping Hao|
|1/11/2019||Hodge-Tate representations and the decomposition theorem.||
|8/11/2019||NO TALK (due to YRANT 2019)||--|
|15/11/2019||Formalism of period rings and .||Philippe Michaud-Rogers|
|22/11/2019||and de Rham representations.||Chris Williams|
|29/11/2019||, Crystalline representations, examples from elliptic curves.||Rob Rockwood|
|6/12/2019||Bringing it all back home||TBA|