Moduli Stacks of tale (, )-Modules and the Existence of Crystalline Lifts (Hardcover)

Matthew Emerton

ISBN 10: 0691241341 / ISBN 13: 9780691241340

Published by Princeton University Press, New Jersey, 2022

About this Item

Hardcover. A foundational account of a new construction in the p-adic Langlands correspondenceMotivated by the p-adic Langlands program, this book constructs stacks that algebraize Mazurs formal deformation rings of local Galois representations. More precisely, it constructs Noetherian formal algebraic stacks over Spf Zp that parameterize etale (, G)-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 BreuilMezard conjecture. Along the way, it proves a number of foundational results in p-adic Hodge theory that may be of independent interest. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9780691241340

Bibliographic Details

• Title: Moduli Stacks of tale (, )-Modules and the Existence of Crystalline Lifts (Hardcover)
• Publisher: Princeton University Press, New Jersey
• Publication Date: 2022
• Language: English
• ISBN 10: 0691241341
• ISBN 13: 9780691241340
• Binding: Hardcover
• Condition: new

About this title

Synopsis

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.

About the Author

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