The structure of generic tame type Galois deformation rings
The structure of generic tame type Galois deformation rings
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Bao Le Hung, IAS
Deformation spaces of representations of Galois groups of p-adic听fields with p-adic Hodge theoretic conditions play a central role in many听arithmetic questions, such as the weight part of Serre's conjecture and听modularity lifting theorems, yet they remain poorly understood in most听situations, especially in dimension >2. I will describe how (some of) these听deformation spaces can be algebraized to nice finite algebraic varieties,听and how this allows one to deduce structural properties about them, such as听the geometric Breuil-Mezard conjecture. This is joint work in progress with听D. Le, B. Levin and S. Morra.