Local model theory for non-generic tame potentially Barsotti--Tate deformation rings

2023/11/28 by Hung, Bao Viet Le, Mézard, Ariane, Morra, Stefano
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2311.16617

Abstract

We develop a local model theory for moduli stacks of 2-dimensional non-scalar tame potentially Barsotti--Tate Galois representations of the Galois group of an unramified extension of ℚ_p. We derive from this explicit presentations of potentially Barsotti--Tate deformation rings, allowing us to prove structural results about them, and prove various conjectures formulated by Caruso--David--Mézard.

Related

• Un calcul d'anneaux de déformations potentiellement Barsotti--Tate
• Local models for Galois deformation rings and applications
• Emerton--Gee stacks, Serre weights, and Breuil--Mézard conjectures for GSp₄
• Modularity of some potentially Barsotti-Tate Galois representations
• Serre weights, Galois deformation rings, and local models