A mod $p$ Jacquet-Langlands Relation and Serre Filtration via the Geometry of Hilbert Modular Varieties Splicing and Dicing

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Free Download Fred Diamond, Payman Kassaei, et al., "A mod $p$ Jacquet-Langlands Relation and Serre Filtration via the Geometry of Hilbert Modular Varieties: Splicing and Dicing"
English | ISBN: 2856299695 | 2023 | 123 pages | PDF | 2 MB
Abstract. - 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 GL2 in characteristic p and generalizes a result of Serre for classical modular forms.
Finally we 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.

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