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A mod p Jacquet-Langlands relation and Serre filtration via the geometry of Hilbert modular varieties : splicing and dicing
We consider Hilbert modular varieties in characteristic p with Iwahori level at p and construct a geometric Jacquet-Langlands relation showing that the irreducible components are isomorphic to products of projective bundles over quaternionic Shimura varieties of level prime to p. We use this to esta...
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| Auteurs principaux : | , , |
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| Format : | Livre |
| Langue : | anglais |
| Titre complet : | A mod p Jacquet-Langlands relation and Serre filtration via the geometry of Hilbert modular varieties : splicing and dicing / Fred Diamond, Payman Kassaei & Shu Sasaki |
| Publié : |
Paris :
Société mathématique de France
, DL 2023 |
| Description matérielle : | 1 vol. (111 p.) |
| Collection : | Astérisque ; 439 |
| Sujets : | |
| Documents associés : | Autre format:
A mod p Jacquet-Langlands relation and Serre filtration via the geometry of Hilbert modular varieties Fait partie de l'ensemble: Astérisque |
| Résumé : | We consider Hilbert modular varieties in characteristic p with Iwahori level at p and construct a geometric Jacquet-Langlands relation showing that the irreducible components are isomorphic to products of projective bundles over quaternionic Shimura varieties of level prime to p. We use this to establish a relation between mod p Hilbert and quaternionic modular forms that reflects the representation theory of GL_2 in characteristic p and generalizes a result of Serre for classical modular forms. Finally we study the fibres of the degeneracy map to level prime to p and prove a cohomological vanishing result that is used to associate Galois representations to mod p Hilbert modular forms |
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| Historique des publications : | N° de : "Astérisque", ISSN 0303-1179, (2023)n°439 |
| Bibliographie : | Bibliographie pages [109]-111 |
| ISBN : | 978-2-85629-969-2 |