Moduli Stacks of Etale ( , )-Modules and the Existence of Crystalline Lifts: (AMS-215)

This book develops stacks that algebraize Mazurs formal deformation rings of local Galois representations, providing a foundation for the p-adic Langlands correspondence. It shows that all mod p representations of the absolute Galois group of a p-adic local field lift to characteristic zero, and discusses the relationship between the geometry of these stacks and the Breuil–Mézard conjecture.

Format: Hardback
Length: 312 pages
Publication date: 13 December 2022
Publisher: Princeton University Press

This book is a groundbreaking exploration into the realm of the p-adic Langlands correspondence, a program that aims to algebraize the formal deformation rings of local Galois representations. Driven by this program, the author constructs a series of Noetherian formal algebraic stacks over the complex numbers Spf Z p, which parameterize étale (ϕ, Γ)-modules. These stacks are then utilized to demonstrate that all mod p representations of the absolute Galois group of a p-adic local field can be lifted to characteristic zero, and indeed, admit crystalline lifts.

The book provides an explicit description of the irreducible components of the underlying reduced substacks and delves into the intricate relationship between the geometry of these stacks and the renowned Breuil–Mézard conjecture. Throughout the journey, the author uncovers a multitude of foundational results in p-adic Hodge theory that possess independent significance.

This comprehensive work serves as a vital resource for researchers and scholars in the field of p-adic mathematics, offering a deep understanding of the underlying principles and providing new insights into the complex dynamics of the p-adic Langlands correspondence.

Dimension: 235 x 156 (mm)
ISBN-13: 9780691241340