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15 June 2019 Tate cycles on some quaternionic Shimura varieties mod p
Yichao Tian, Liang Xiao
Duke Math. J. 168(9): 1551-1639 (15 June 2019). DOI: 10.1215/00127094-2018-0068

Abstract

Let F be a totally real field in which a prime number p>2 is inert. We continue the study of the (generalized) Goren–Oort strata on quaternionic Shimura varieties over finite extensions of Fp. We prove that, when the dimension of the quaternionic Shimura variety is even, the Tate conjecture for the special fiber of the quaternionic Shimura variety holds for the cuspidal π-isotypical component, as long as the two unramified Satake parameters at p are not differed by a root of unity.

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Yichao Tian. Liang Xiao. "Tate cycles on some quaternionic Shimura varieties mod p." Duke Math. J. 168 (9) 1551 - 1639, 15 June 2019. https://doi.org/10.1215/00127094-2018-0068

Information

Received: 25 May 2017; Revised: 30 October 2018; Published: 15 June 2019
First available in Project Euclid: 12 June 2019

zbMATH: 07097310
MathSciNet: MR3961211
Digital Object Identifier: 10.1215/00127094-2018-0068

Subjects:
Primary: 11G18
Secondary: 11F41, 14C25, 14G35

Rights: Copyright © 2019 Duke University Press

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Vol.168 • No. 9 • 15 June 2019
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