Moduli stacks of étale ([phi], [Gamma])-modules and the existence of crystalline lifts / Matthew Emerton, Toby Gee.

Format:

Book

Author/Creator:

Emerton, Matthew, author.

Gee, Toby, 1980- author.

Series:

Annals of mathematics studies ; no. 215.

Annals of mathematics studies ; number 215

Language:

English

Subjects (All):

Algebraic stacks.

Moduli theory.

Geometry, Algebraic.

Physical Description:

ix, 298 pages : illustrations ; 25 cm.

Place of Publication:

Princeton : Princeton University Press, 2023.

Summary:

"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 ([phi], [Gamma])-modules; the formal completions of these stacks at points in their special fibres recover the universal deformation rings of local Galois representations. Matthew Emerton and Toby Gee 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. They explicitly describe the irreducible components of the underlying reduced substacks and discuss the relationship between the geometry of these stacks and the Breuil-Mézard conjecture. Along the way, they prove a number of foundational results in p-adic Hodge theory that may be of independent interest"-- Provided by publisher.

Contents:

Rings and coefficients

Moduli stacks of [phi]-modules and ([phi], [Gamma])-modules

Crystalline and semistable moduli stacks

Families of extensions

Crystalline lifts and the finer structure of Xd,red

The rank one case

A geometric Breuil-Mézard conjecture.

Notes:

Includes bibliographical references (pages 289-296) and index.

Other Format:

Online version: Emerton, Matthew. Moduli stacks of étale ([phi], [Gamma])-modules and the existence of crystalline lifts

ISBN:

9780691241340

0691241341

9780691241357

069124135X

OCLC:

1341481977