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Strata Hasse invariants, Hecke algebras and Galois representations
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 22019 (English)In: Inventiones Mathematicae, ISSN 0020-9910, E-ISSN 1432-1297, Vol. 217, no 3, p. 887-984Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2019. Vol. 217, no 3, p. 887-984
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-173095DOI: 10.1007/s00222-019-00882-5ISI: 000478909700004OAI: oai:DiVA.org:su-173095DiVA, id: diva2:1358046
Available from: 2019-10-07 Created: 2019-10-07 Last updated: 2019-10-07Bibliographically approved

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