Wednesday, June 7, 2023
10:00 a.m. (sharp)

Zoom Web Conference

PhD Candidate: Heejong Lee
Supervisor: Florian Herzig
Thesis title: Emerton–Gee stacks, Serre weights, and Breuil–Mézard conjectures for GSp4

PhD Defense – Lee


We construct a moduli stack of rank 4 symplectic projective etale ´ (ϕ, Γ)-modules and prove its geometric
properties for any prime p > 2 and finite extension K/Qp. When K/Qp is unramified, we adapt the theory of local models recently developed by Le–Le Hung–Levin–Morra to study the geometry of potentially crystalline substacks in this stack. In particular, we prove the unibranch property at torus fixed points of local models and deduce that tamely potentially crystalline deformation rings are domain under genericity conditions. As applications, we prove, under appropriate genericity conditions, an GSp4-analogue of the Breuil–Mezard conjecture for tamely potentially crystalline deformation rings, the weight part of Serre’s conjecture formulated by Gee–Herzig–Savitt for global Galois representations valued in GSp4 satisfying Taylor–Wiles conditions, and a modularity lifting result for tamely potentially crystalline representations.


The draft of the thesis can be found here: Heejong_Lee_thesis


no comment as of now

Sorry, comments closed.