Moduli Stacks of Etale ( , )-Modules and the Existence of Crystalline Lifts: (AMS-215) - Matthew Emerton; Toby Gee; | Foyles Bookstore
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Moduli Stacks of Etale ( ,  )-Modules and the Existence of Crystalline Lifts: (AMS-215)
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Moduli Stacks of Etale ( , )-Modules and the Existence of Crystalline Lifts: (AMS-215) (Hardback)

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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 etale ( , )-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-Mezard conjecture. Along the way, it proves a number of foundational results in p-adic Hodge theory that may be of independent interest.

Science & MathematicsMathematicsGeometryAlgebraic geometry Publisher: Princeton University Press Publication Date: 13/12/2022 ISBN-13: 9780691241340  Details: Type: Hardback Format: Books
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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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