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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 : | , , |
|---|---|
| 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 |
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| 200 | 1 | |a A mod p Jacquet-Langlands relation and Serre filtration via the geometry of Hilbert modular varieties |e splicing and dicing |f Fred Diamond, Payman Kassaei & Shu Sasaki | |
| 214 | 0 | |a Paris |c Société mathématique de France |d DL 2023 | |
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| 305 | |a N° de : "Astérisque", ISSN 0303-1179, (2023)n°439 | ||
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| 330 | |a 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 |2 4e de couverture | ||
| 359 | 2 | |b Shimura varieties |b Automorphic vector bundles |b Iwahori level structures |b A Jacquet-Langlands relation |b The Serre Filtration |b Degeneracy fibers | |
| 452 | | | |0 272107425 |t A mod p Jacquet-Langlands relation and Serre filtration via the geometry of Hilbert modular varieties |o splicing and dicing |f Fred Diamond, Payman Kassaei & Shu Sasaki |d 2023 |c Paris |n Société mathématique de France | |
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