Author(s): Chol Park (박 철), Zicheng Qian (钱子诚)
Series: Memoires de la Société Mathématique de France 173
Publisher: Société Mathématique de France
Year: 2022
Language: English
Pages: 150
Chapter 1. Introduction
1.1. Local Galois side
1.2. Local automorphic side
1.3. Weight elimination and automorphy of a Serre weight
1.4. Mod p local-global compatibility
1.5. Notation
Acknowledgements
Chapter 2. Integral p-adic Hodge theory
2.1. Filtered (,N)-modules with descent data
2.2. Strongly divisible modules with descent data
2.3. Breuil modules with descent data
2.4. Linear algebra with descent data
2.5. Fontaine-Laffaille modules
2.6. Étale -modules
Chapter 3. Local Galois side
3.1. Elimination of Galois types
3.2. Fontaine-Laffaille parameters
3.3. Breuil modules of certain inertial types of niveau 1
3.4. Fontaine-Laffaille parameters vs Frobenius eigenvalues
3.5. Filtration of strongly divisible modules
3.6. Reducibility of certain lifts
3.7. Main results on the Galois side
Chapter 4. Local automorphic side
4.1. Jacobi sums in characteristic p
4.2. Summary of results on Deligne-Lusztig representations
4.3. A multiplicity one theorem
4.4. Jacobi sums in characteristic 0
4.5. Special vectors in a dual Weyl module
4.6. Some technical formula
4.7. A non-vanishing theorem
4.8. Main results in characteristic p
Chapter 5. Mod p local-global compatibility
5.1. The space of algebraic automorphic forms
5.2. Serre weights and potentially crystalline lifts
5.3. Weight elimination and automorphy of a Serre weight
5.4. Some application of Morita theory
5.5. Generalization of Chapter 4
5.6. Main results
Bibliography
