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Stratifications of Flag Spaces and Functoriality
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 22019 (English)In: International mathematics research notices, ISSN 1073-7928, E-ISSN 1687-0247, Vol. 2019, no 12, p. 3646-3682Article in journal (Refereed) Published
Abstract [en]

We define stacks of zip flags, which form towers above the stack of G-zips of Moonen, Pink, Wedhorn and Ziegler in [14-16]. A stratification is defined on the stack of zip flags, and principal purity is established under a mild assumption on the underlying prime p. We generalize flag spaces of Ekedahl-Van der Geer [4] and relate them to stacks of zip flags. For large p, it is shown that strata are affine. We prove that morphisms with central kernel between stacks of G-zips have discrete fibers. This allows us to prove principal purity of the zip stratification for maximal zip data. The latter provides a new proof of the existence of Hasse invariants for Ekedahl-Oort strata of good reduction Shimura varieties of Hodge-type, first proved in [8].

Place, publisher, year, edition, pages
2019. Vol. 2019, no 12, p. 3646-3682
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-176634DOI: 10.1093/imrn/rnx229ISI: 000493547500002OAI: oai:DiVA.org:su-176634DiVA, id: diva2:1381734
Available from: 2019-12-27 Created: 2019-12-27 Last updated: 2019-12-27Bibliographically approved

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