Moduli Stacks of Étale (ϕ, Γ)-Modules and the Existence of 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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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.

SKU: 9780691241357
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Weight 1 kg
Dimensions 23 × 15 × 1 cm
Book Author

Matthew Emerton, Toby Gee

Edition

1st

Format

Paperback

ISBN

9780691241357

Language

English

Pages

312

Publication Year

Publisher

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