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

• Verfasst von: Diamond, Fred [VerfasserIn]
• Verfasst von: Kassaei, Payman L. [VerfasserIn]
• Verfasst von: Sasaki, Shu [VerfasserIn]
• Titel: A mod p Jacquet-Langlands relation and Serre filtration via the geometry of Hilbert modular varieties
• Titelzusatz: splicing and dicing
• Verf.angabe: Fred Diamond, Payman Kassaei & Shu Sasaki
• Verlagsort: Paris
• Verlag: Société Mathématique de France
• Jahr: 2023
• Umfang: 111 Seiten
• Illustrationen: Diagramme
• Format: 24 cm
• Gesamttitel/Reihe: Astérisque ; 439 (2023)
• Fussnoten: Literaturverzeichnis: Seite 109-111
• Schrift/Sprache: Zusammenfassung in französischer und englischer Sprache
• ISBN: 978-2-85629-969-2
• Schlagwörter: (s)Hilbertsche Modulform / (s)Hilbertsche Modulfläche / (s)Projektives Bündel / (s)Quaternion / (s)Galois-Darstellung
• Sprache: eng
• RVK-Notation: SI 832
• K10plus-PPN: 1853570400

Abstract

Publisher’s description: 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 modp Hilbert and quaternionic modular forms that reflects the representation theory of GL2 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 modp Hilbert modular forms.