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2017 Tate cycles on some unitary Shimura varieties mod $p$
David Helm, Yichao Tian, Liang Xiao
Algebra Number Theory 11(10): 2213-2288 (2017). DOI: 10.2140/ant.2017.11.2213

Abstract

Let F be a real quadratic field in which a fixed prime p is inert, and E 0 be an imaginary quadratic field in which p splits; put E = E 0 F . Let X be the fiber over F p 2 of the Shimura variety for G ( U ( 1 , n 1 ) × U ( n 1 , 1 ) ) with hyperspecial level structure at p for some integer n 2 . We show that under some genericity conditions the middle-dimensional Tate classes of X are generated by the irreducible components of its supersingular locus. We also discuss a general conjecture regarding special cycles on the special fibers of unitary Shimura varieties, and on their relation to Newton stratification.

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David Helm. Yichao Tian. Liang Xiao. "Tate cycles on some unitary Shimura varieties mod $p$." Algebra Number Theory 11 (10) 2213 - 2288, 2017. https://doi.org/10.2140/ant.2017.11.2213

Information

Received: 17 November 2015; Revised: 24 August 2017; Accepted: 28 September 2017; Published: 2017
First available in Project Euclid: 1 February 2018

zbMATH: 06825450
MathSciNet: MR3744356
Digital Object Identifier: 10.2140/ant.2017.11.2213

Subjects:
Primary: 11G18
Secondary: 11R39, 14C17, 14C25, 14G35

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.11 • No. 10 • 2017
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