A mod p Jacquet-Langlands relation and Serre filtration via the geometry of Hilbert modular varieties: Splicing and dicing 9782856299692

158 109 2MB

English Pages 115 [124] Year 2023

A mod p Jacquet-Langlands relation and Serre filtration via the geometry of Hilbert modular varieties: Splicing and dicing
9782856299692

Author / Uploaded
Fred Diamond
Payman Kassaei
Shu Sasaki

Table of contents :
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

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