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A mod p Jacquet-Langlands relation and Serre filtration via the geometry of Hilbert modular varieties: Splicing and dicing

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Author(s): Fred Diamond, Payman Kassaei, Shu Sasaki
Series: Astérisque 439
Publisher: Société Mathématique de France
Year: 2023

Language: English
Pages: 115

Chapter 1. Introduction
1.1. Overview
1.2. Geometric Jacquet-Langlands
1.3. The Serre filtration
1.4. Degeneracy fibers
1.5. Questions
1.6. Acknowledgments
Chapter 2. Shimura varieties
2.1. Hilbert modular varieties
2.2. Unitary Shimura varieties
2.3. Quaternionic Shimura varieties
Chapter 3. Automorphic vector bundles
3.1. Construction of automorphic vector bundles
3.2. Relations among vector bundles
Chapter 4. Iwahori level structures
4.1. The Hilbert modular setting
4.2. The unitary setting
4.3. Stratifications
Chapter 5. A Jacquet-Langlands relation
5.1. Splicing
5.2. Unitary analogue of the theorem
5.3. Proof of Theorem A
5.4. Comparison of vector bundles
Chapter 6. The Serre filtration
6.1. Dualizing sheaves
6.2. Dicing
6.3. Proof of Theorem B
Chapter 7. Degeneracy fibers
7.1. Frobenius factorization
7.2. Crystallization
7.3. Cohomological vanishing
Bibliography