Strata Hasse invariants, Hecke algebras and Galois representations

• 成果类型: Article
• 署名作者: Goldring, Wushi; Koskivirta, Jean-Stefan
• 署名单位: Stockholm University; University of Tokyo
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-019-00882-5
• 发表日期: 2019
• 页码: 887-984
• 关键词: siegel modular-forms; shimura-varieties; pel-type; ekedahl-oort; mod-p; discrete-series; newton strata; COHOMOLOGY; LIMITS; compactifications

摘要

We construct group-theoretical generalizations of the Hasse invariant on strata closures of the stacks G-Zip(mu). 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(mu), fibered in flag varieties over G-Zip(mu). 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 nondegenerate 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 onmod p modular forms is generalized to general Hodgetype Shimura varieties.