| Softcover ISBN: | 978-2-85629-969-2 |
| Product Code: | AST/439 |
| List Price: | $57.00 |
| AMS Member Price: | $45.60 |
| Softcover ISBN: | 978-2-85629-969-2 |
| Product Code: | AST/439 |
| List Price: | $57.00 |
| AMS Member Price: | $45.60 |
-
Book DetailsAstérisqueVolume: 439; 2023; 602 ppMSC: Primary 11; 14
The authors 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 \(p\). The authors 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 the authors study the fibers 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.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
ReadershipGraduate students and research mathematicians.
-
Additional Material
-
RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
- Book Details
- Additional Material
- Requests
The authors 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 \(p\). The authors 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 the authors study the fibers 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.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Graduate students and research mathematicians.
