Screen LibraryModuli stacks of étale ([phi], [Gamma])-modules and the existence of crystalline lifts /
"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 ([phi], [Gamma])-modules; the forma...
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| Main Authors: | |
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| Published: |
Princeton University Press,
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| Publisher Address: | Princeton : |
| Publication Dates: | 2023. |
| Literature type: | Book |
| Language: | English |
| Series: |
Annals of mathematics studies ;
number 215 |
| Subjects: | |
| Summary: |
"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 ([phi], [Gamma])-modules; the formal completions of these stacks at points in their special fibres recover the universal deformation rings of local Galois representations. Matthew Emerton and Toby Gee use these stacks 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. They explicitly describe the irreducible components of the underlying reduced substacks and discuss the relationship between the geometry of these stacks and the Breuil-Mézard conjecture. Along the way, they prove a number of foundational results in p-adic Hodge theory that may be of independent interest"-- |
| Carrier Form: | ix, 298 pages : illustrations ; 24 cm. |
| Bibliography: | Includes bibliographical references (pages [289]-296) and index. |
| ISBN: |
9780691241340 0691241341 |
| Index Number: | QA564 |
| CLC: | O189.2 |
| Call Number: | O189.2/E537 |
| Contents: | Rings and coefficients -- Moduli stacks of [phi]-modules and ([phi], [Gamma])-modules -- Crystalline and semistable moduli stacks -- Families of extensions -- Crystalline lifts and the finer structure of Xd,red -- The rank one case -- A geometric Breuil-Mézard conjecture. |