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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Moduli Stacks of Étale (ϕ, Γ)-Modules and the Existence of Crystalline Lifts

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

Emerton, Matthew
Gee, Toby

Hardcover

Series: Annals of Mathematics Studies, Book 215

General MathematicsGeometry

ISBN10: 0691241341
ISBN13: 9780691241340
Publisher: Princeton University Press
Published: Dec 13 2022
Pages: 312
Weight: 1.32
Height: 0.90 Width: 6.10 Depth: 9.30
Language: English

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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