论文标题
Mod P Jacquet-Langlands的关系和通过Hilbert模块化品种的几何形状进行过滤：剪接和挖掘
A mod p Jacquet-Langlands relation and Serre filtration via the geometry of Hilbert modular varieties: Splicing and dicing
论文作者
论文摘要
我们考虑在P的特征P中具有Hilbert模块化品种，并构建了几何Jacquet-Langlands关系，表明不可减至的组件与Quaternionic bughtions shimura shimura shimura品种的产品构成同构成。我们使用它来建立Mod P Hilbert与Quaternionic模块化形式之间的关系，该模块形式反映了特征P中GL_2的表示理论，并概括了经典模块化形式的Serre的结果。最后，我们研究了脱落图图的纤维以将Prime升至p，并证明了共同的消失结果，该结果用于将Galois表示与Mod P Hilbert模块化形式相关联。
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.
