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15 May 2022 Honda–Tate theory for Shimura varieties
Mark Kisin, Keerthi Madapusi Pera, Sug Woo Shin
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Duke Math. J. 171(7): 1559-1614 (15 May 2022). DOI: 10.1215/00127094-2021-0063

Abstract

A Shimura variety of Hodge type is a moduli space for abelian varieties equipped with a certain collection of Hodge cycles. We show that the Newton strata on such varieties are nonempty provided that the corresponding group G is quasisplit at p, confirming a conjecture of Fargues and Rapoport in this case. Under the same condition, we conjecture that every mod p isogeny class on such a variety contains the reduction of a special point. This is a refinement of Honda–Tate theory. We prove a large part of this conjecture for Shimura varieties of PEL type. Our results make no assumption on the availability of a good integral model for the Shimura variety. In particular, the group G may be ramified at p.

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Mark Kisin. Keerthi Madapusi Pera. Sug Woo Shin. "Honda–Tate theory for Shimura varieties." Duke Math. J. 171 (7) 1559 - 1614, 15 May 2022. https://doi.org/10.1215/00127094-2021-0063

Information

Received: 18 August 2018; Revised: 4 June 2021; Published: 15 May 2022
First available in Project Euclid: 19 April 2022

Digital Object Identifier: 10.1215/00127094-2021-0063

Subjects:
Primary: 11G18
Secondary: 14G35

Keywords: abelian varieties , p-divisible groups , Shimura varieties

Rights: Copyright © 2022 Duke University Press

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Vol.171 • No. 7 • 15 May 2022
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