Moduli Stacks of Étale (ϕ, Γ)-Modules and the Existence of Crystalline Lifts: (Ams-215) by Emerton, Matthew
Moduli Stacks of Étale (ϕ, Γ)-Modules and the Existence of Crystalline Lifts: (Ams-215) by Emerton, Matthew

Moduli Stacks of Étale (ϕ, Γ)-Modules and the Existence of Crystalline Lifts: (Ams-215)

A foundational account of a new construction in the p-adic Langlands correspondence Motivated by the p-adic Langlands...
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$573.27 SGD
SKU: 9780691241340
Product Type: Books
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Author: Matthew Emerton
Format: Hardcover
Language: English
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Moduli Stacks of Étale (ϕ, Γ)-Modules and the Existence of Crystalline Lifts: (Ams-215) by Emerton, Matthew

Moduli Stacks of Étale (ϕ, Γ)-Modules and the Existence of Crystalline Lifts: (Ams-215)

$573.27
Moduli Stacks of Étale (ϕ, Γ)-Modules and the Existence of Crystalline Lifts: (Ams-215) by Emerton, Matthew

Moduli Stacks of Étale (ϕ, Γ)-Modules and the Existence of Crystalline Lifts: (Ams-215)

$573.27
Author: Matthew Emerton
Format: Hardcover
Language: English
Description

A foundational account of a new construction in the p-adic Langlands correspondence

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.

Author: Matthew Emerton, Toby Gee
Publisher: Princeton University Press
Published: 12/13/2022
Pages: 312
Binding Type: Hardcover
Weight: 1.32lbs
Size: 9.30h x 6.10w x 0.90d
ISBN: 9780691241340
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