Moduli Stacks of Étale (ϕ, Γ)-Modules and the Existence of Crystalline Lifts: (AMS-215) (Annals of Mathematics Studies, 215) - Image 1

£101.25

Princeton University Press Moduli Stacks of Étale (ϕ, Γ)-Modules and the Existence of Crystalline Lifts: (AMS-215) (Annals of Mathematics Studies, 215)

Name: Moduli Stacks of Etale ( , )-Modules and the Existence of Crystalline Lifts: (AMS-215) (Annals of Mathematics Studies, 215)
Brand: Princeton University Press
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Geometry & Topology

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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.

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Brand: Princeton University Press
Format: Hardcover
ASIN: 0691241341
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Geometry & Topology
Domain: Amazon UK
Release Date: 13 December 2022
Listed Since: 22 January 2022

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Princeton University Press Moduli Stacks of Étale (ϕ, Γ)-Modules and the Existence of Crystalline Lifts: (AMS-215) (Annals of Mathematics Studies, 215)

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