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# memo_has_moved_text();Deformation Theory and Local-Global Compatibility of Langlands Correspondences

Martin Luu

Publication: Memoirs of the American Mathematical Society
Publication Year: 2015; Volume 238, Number 1123
ISBNs: 978-1-4704-1422-1 (print); 978-1-4704-2609-5 (online)
DOI: http://dx.doi.org/10.1090/memo/1123
Published electronically: February 23, 2015
Keywords:Local-global compatibility

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Chapters

• Preface
• Chapter 1. Introduction
• Chapter 2. Preliminaries
• Chapter 3. Local-global compatibility for Hilbert Modular Forms
• Chapter 4. Local-global compatibility results via crystalline periods
• Chapter 5. Local semi-simplifications: The case of general linear groups
• Chapter 6. Local semi-simplifications: The case of symplectic groups
• Chapter 7. Congruences
• Chapter 8. Local monodromy operators: The case of general linear groups
• Chapter 9. Local monodromy operators: The case of symplectic groups

### Abstract

The deformation theory of automorphic representations is used to study local properties of Galois representations associated to automorphic representations of general linear groups and symplectic groups. In some cases this allows to identify the local Galois representations with representations predicted by a local Langlands correspondence.