Algebra & Number Theory
- Algebra Number Theory
- Volume 11, Number 10 (2017), 2213-2288.
Tate cycles on some unitary Shimura varieties mod $p$
Let be a real quadratic field in which a fixed prime is inert, and be an imaginary quadratic field in which splits; put . Let be the fiber over of the Shimura variety for with hyperspecial level structure at for some integer . We show that under some genericity conditions the middle-dimensional Tate classes of 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.
Algebra Number Theory, Volume 11, Number 10 (2017), 2213-2288.
Received: 17 November 2015
Revised: 24 August 2017
Accepted: 28 September 2017
First available in Project Euclid: 1 February 2018
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: 11R39: Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E55] 14C17: Intersection theory, characteristic classes, intersection multiplicities [See also 13H15] 14C25: Algebraic cycles 14G35: Modular and Shimura varieties [See also 11F41, 11F46, 11G18]
Helm, David; Tian, Yichao; Xiao, Liang. Tate cycles on some unitary Shimura varieties mod $p$. Algebra Number Theory 11 (2017), no. 10, 2213--2288. doi:10.2140/ant.2017.11.2213. https://projecteuclid.org/euclid.ant/1517454184