Strata Hasse不变量、Hecke代数和伽罗瓦表示
Strata Hasse invariants, Hecke algebras and Galois representations
摘要：
我们构造了关于栈$G$ -Zip $^μ$的层闭包的Hasse不变量的群论推广。限制到zip数据的Hodge型，我们得到了一个群论Hasse不变量的一般Hodge型Shimura簇的每个Ekedahl-Oort层闭包。一个关键的工具是构造一个zip标志$G$ -ZipFlag $^μ$的堆栈，这些标志在$G$ -Zip $^μ$上以各种标志形式进行纤维化。它提供了一个同时推广的“经典情况”齐性复流形研究的格里菲斯-施密德和“旗空间”西格尔品种研究的埃克达尔-范德格尔。获得了四种应用：（1）在模素幂的Hodge型Shimura簇的凝聚上同调上附加了伪表示。(2)伽罗瓦表示与离散级数阿基米德分量的许多具有非退化极限的自守表示相联系。(3)证明了Hodge型Shimura簇的极小紧化中的所有Ekedahl-Oort层都是仿射的，从而证明了Oort的一个猜想。(4)Serre给泰特的信中关于模$p$模形式的一部分被推广到一般的Hodge型Shimura簇。
英文摘要：
We construct group-theoretical generalizations of the Hasse invariant on strata closures of the stacks $G$-Zip$^μ$. Restricting to zip data of Hodge type, we obtain a group-theoretical Hasse invariant on every Ekedahl-Oort stratum closure of a general Hodge-type Shimura variety. A key tool is the construction of a stack of zip flags $G$-ZipFlag$^μ$, fibered in flag varieties over $G$-Zip$^μ$. It provides a simultaneous generalization of the "classical case" homogeneous complex manifolds studied by Griffiths-Schmid and the "flag space" for Siegel varieties studied by Ekedahl-van der Geer. Four applications are obtained: (1) Pseudo-representations are attached to the coherent cohomology of Hodge-type Shimura varieties modulo a prime power. (2) Galois representations are associated to many automorphic representations with non-degenerate limit of discrete series archimedean component. (3) It is shown that all Ekedahl-Oort strata in the minimal compactification of a Hodge-type Shimura variety are affine, thereby proving a conjecture of Oort. (4) Part of Serre's letter to Tate on mod $p$ modular forms is generalized to general Hodge-type Shimura varieties.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
