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

Emerton, Matthew; Gee, Toby

 
9780691241357: Moduli Stacks of Étale (ϕ, Γ)-Modules and the Existence of Crystalline Lifts: (AMS-215) (Annals of Mathematics Studies, 215)
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ISBN 10: 069124135X ISBN 13: 9780691241357
Editorial: Princeton University Press, 2022

Sinopsis

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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Acerca del autor

Matthew Emerton is professor of mathematics at the University of Chicago. Toby Gee is professor of mathematics at Imperial College London.

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Editorial
Princeton University Press
Año de publicación
2022
Idioma
Inglés
ISBN 10 
069124135X
ISBN 13 
9780691241357
Encuadernación
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Número de páginas
312
Contacto del fabricante
Princeton University Press
https://press.princeton.edu/books

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no disponible

Otras ediciones populares con el mismo título

9780691241340: Moduli Stacks of Étale (ϕ, Γ)-Modules and the Existence of Crystalline Lifts: (AMS-215) (Annals of Mathematics Studies, 215)

Edición Destacada

ISBN 10:  0691241341 ISBN 13:  9780691241340
Editorial: Princeton University Press, 2022
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