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Moduli stacks of \'etale (phi,Gamma)-modules and the existence of crystalline lifts by Emerton, Matthew; Gee, Toby is a scholarly article available to read on EtoBox.

What is Moduli stacks of \'etale (phi,Gamma)-modules and the existence of crystalline lifts about?

We construct stacks which algebraize Mazur's formal deformation rings of local Galois representations. More precisely, we construct Noetherian formal algebraic stacks over Spf Zp which parameterize \'etale (phi,Gamma)-modules; the formal completions of these stacks at points in their special fibres recover the universal deformation rings of local Galois representations. We use these stacks to show that all mod p representations of the absolute Galois group of a p-adic local field lift to characteristic zero, and indeed admit crystalline lifts. We also discuss the relationship between the geometry of our stacks and the Breuil-M\'ezard conjecture.

Author

Emerton, Matthew; Gee, Toby

Published

2019

Language

EN