Duke Mathematical Journal
- Duke Math. J.
- Volume 168, Number 9 (2019), 1551-1639.
Tate cycles on some quaternionic Shimura varieties mod
Let be a totally real field in which a prime number is inert. We continue the study of the (generalized) Goren–Oort strata on quaternionic Shimura varieties over finite extensions of . 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 -isotypical component, as long as the two unramified Satake parameters at are not differed by a root of unity.
Duke Math. J., Volume 168, Number 9 (2019), 1551-1639.
Received: 25 May 2017
Revised: 30 October 2018
First available in Project Euclid: 12 June 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11G18: Arithmetic aspects of modular and Shimura varieties [See also 14G35]
Secondary: 14G35: Modular and Shimura varieties [See also 11F41, 11F46, 11G18] 14C25: Algebraic cycles 11F41: Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20]
Tian, Yichao; Xiao, Liang. Tate cycles on some quaternionic Shimura varieties mod $p$. Duke Math. J. 168 (2019), no. 9, 1551--1639. doi:10.1215/00127094-2018-0068. https://projecteuclid.org/euclid.dmj/1560326497