Skip to Main Content

Moduli Stacks of Étale (f, G)-Modules and the Existence of Crystalline Lifts: (AMS-215)

Online ISBN:
9780691241364
Print ISBN:
9780691241357
Publisher:
Princeton University Press
Book

Moduli Stacks of Étale (f, G)-Modules and the Existence of Crystalline Lifts: (AMS-215)

Matthew Emerton,
Matthew Emerton
University of Chicago
Find on
Toby Gee
Toby Gee
Imperial College London
Find on
Published online:
21 September 2023
Published in print:
13 December 2022
Online ISBN:
9780691241364
Print ISBN:
9780691241357
Publisher:
Princeton University Press

Abstract

Motivated by the p-adic Langlands program, this book constructs stacks that algebraize Mazur's formal deformation rings of local Galois representations. More precisely, it constructs Noetherian formal algebraic stacks over Spf Zp that parameterize étale (ϕ‎, Γ‎)-modules; the formal completions of these stacks at points in their special fibres recover the universal deformation rings of local Galois representations. These stacks are then used 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. The book explicitly describes the irreducible components of the underlying reduced substacks and discusses the relationship between the geometry of these stacks and the Breuil–Mézard conjecture. Along the way, it proves a number of foundational results in p-adic Hodge theory that may be of independent interest.

Contents
Close
This Feature Is Available To Subscribers Only

Sign In or Create an Account

Close

This PDF is available to Subscribers Only

View Article Abstract & Purchase Options

For full access to this pdf, sign in to an existing account, or purchase an annual subscription.

Close