Description: 

The workshop series focuses on the recent work of Emerton and Gee, who constructed a formal algebraic stack of p-adic Galois representations for a finite extension of Qp. This concept is an algebra analogue of the formal deformation space introduced by Mazur. The construction of Emerton--Gee has immediate applications to topics such as crystalline lifting of Galois representations, and Serre weight conjectures.  

This one-day workshop is the third and the last in this series, which aims to prove important properties and applications of the Emerton-Gee stacks, including structure of its reduced substack, construction of semistable deformation stack with prescribed tame type, and relation to the Breuil-Mezard conjecture. We hope the workshop brings this interesting theory to researchers in related area, and explore possible new projects and collaborations. This workshop consists of four introductory lectures. On October 16 (Wednesday), there will be two related presentations at Morningside center on the same topic.

Reference:

[EG] M. Emerton and T. Gee, Moduli stacks of etale (phi, Gamma)-modules and the existence of crystalline lifts.

Organizers: Yiwen Ding, Yongquan Hu, and Liang Xiao

Schedule:  

Speaker: Yiwen Ding (BICMR)  

Title: Dimensions of families of extensions  

Abstract: We calculate the dimensions of families of extensions inside Emerton-Gee stacks (5.4), and we show that the moduli spaces of maximally non-split extensions of rank 1 (phi, Gamma)-modules constitute all irreducible components of the reduced substack of the Emerton-Gee stack (of maximal dimension) (5.5).

Speaker: Hui Gao (Southern University of Science and Technology)  

Title: Semistable substack 

Abstract: I will explain section 4, where they construct the semi-stable substack.

Speaker: Yongquan Hu (Morningside Center of Mathematics)  

Title: Breuil-Mezard conjecture in terms of Emerton-Gee stack  

Abstract: I will explain a reformulation of Breuil-Mezard conjecture in terms of Emerton-Gee stack.

Speaker: Liang Xiao (BICMR)  

Title: Existence of crystalline lift  

Abstract: I will explain section 6 of [EG], in which they prove the existence of potentially diagonalizable crystalline lifts for a given residual local Galois representation.