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1 October 2021 EKOR strata for Shimura varieties with parahoric level structure
Xu Shen, Chia-Fu Yu, Chao Zhang
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Duke Math. J. 170(14): 3111-3236 (1 October 2021). DOI: 10.1215/00127094-2021-0047

Abstract

We study the geometry of reduction modulo p of the Kisin–Pappas integral models for certain Shimura varieties of abelian type with parahoric level structure. We give some direct and geometric constructions for the EKOR (Ekedahl–Kottwitz–Oort–Rapoport) strata on these Shimura varieties, using the theories of G-zips and mixed characteristic local G-Shtukas. We establish several basic properties of these strata, including the smoothness, dimension formula, and closure relation. Moreover, we apply our results to the study of Newton strata and central leaves on these Shimura varieties.

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Xu Shen. Chia-Fu Yu. Chao Zhang. "EKOR strata for Shimura varieties with parahoric level structure." Duke Math. J. 170 (14) 3111 - 3236, 1 October 2021. https://doi.org/10.1215/00127094-2021-0047

Information

Received: 5 November 2019; Revised: 10 October 2020; Published: 1 October 2021
First available in Project Euclid: 10 September 2021

Digital Object Identifier: 10.1215/00127094-2021-0047

Subjects:
Primary: 14G35
Secondary: 11G18

Keywords: G-zips , local models , Shimura varieties , Shtukas , stratifications

Rights: Copyright © 2021 Duke University Press

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Vol.170 • No. 14 • 1 October 2021
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