The Ruth Moufang Lectures will have their third iteration on December 7th and 8th, 2023 in Heidelberg. We are happy to announce that our speaker will be Ariane Mézard (Sorbonne Université).

Ariane Mézard – Seminars talks “Potentially Barsotti-Tate deformations rings I and II”

Abstract: 
Deformation of Galois representations in an efficient tool in arithmetic geometry. Within the framework of p-adic Hodge theory, it opened the way towards a p-adic Langlands program. In my first talk, I will present briefly the general setting and open questions for some certain geometric Galois representations. In dimension two, a computational approach, in collaboration with X. Caruso and A. David, allow us to formulate conjectures in the potentially Barsotti-Tate case.

In my second talk, I will present a local model theory for moduli stacks of étale (Phi,Gamma)-modules corresponding to 2-dimensional non-scalar tame potentially Barsotti-Tate Galois representations of the Galois group of an unramified extension of Qp. From this work, in collaboration with B.
Le Hung and S. Morra, we derive explicit presentations of potentially Barsotti-Tate deformation rings, in particular the proof of the Caruso-David-Mézard conjectures.