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15 October 2020 Mod p isogeny classes on Shimura varieties with parahoric level structure
Rong Zhou
Duke Math. J. 169(15): 2937-3031 (15 October 2020). DOI: 10.1215/00127094-2020-0021

Abstract

We study the special fiber of the integral model for Shimura varieties of Hodge type with parahoric level structure recently constructed by Kisin and Pappas. We show that when the group at p is residually split, the points in the mod p isogeny classes have the form predicted by the Langlands–Rapoport conjecture. We also verify most of the He–Rapoport axioms for these integral models without the residually split assumption. This allows us to prove that all Newton strata are nonempty for these models. The verification of the axioms in full is reduced to a question on the connected components of affine Deligne–Lusztig varieties.

Citation

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Rong Zhou. "Mod p isogeny classes on Shimura varieties with parahoric level structure." Duke Math. J. 169 (15) 2937 - 3031, 15 October 2020. https://doi.org/10.1215/00127094-2020-0021

Information

Received: 15 February 2018; Revised: 22 November 2019; Published: 15 October 2020
First available in Project Euclid: 10 September 2020

MathSciNet: MR4158671
Digital Object Identifier: 10.1215/00127094-2020-0021

Subjects:
Primary: 11A99
Secondary: 14G35

Rights: Copyright © 2020 Duke University Press

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Vol.169 • No. 15 • 15 October 2020
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