Vol. 11, No. 10, 2017

Download this article
Download this article For screen
For printing
Recent Issues

Volume 12
Issue 5, 1001–1309
Issue 4, 751–999
Issue 3, 493–750
Issue 2, 227–492
Issue 1, 1–225

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editors' Addresses
Editors' Interests
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Author Index
To Appear
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Tate cycles on some unitary Shimura varieties mod $p$

David Helm, Yichao Tian and Liang Xiao

Vol. 11 (2017), No. 10, 2213–2288
Abstract

Let F be a real quadratic field in which a fixed prime p is inert, and E0 be an imaginary quadratic field in which p splits; put E = E0F. Let X be the fiber over Fp2 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.

Keywords
Supersingular locus, Special fiber of Shimura varieties, Deligne–Lusztig varieties, Tate conjecture
Mathematical Subject Classification 2010
Primary: 11G18
Secondary: 11R39, 14C17, 14C25, 14G35
Milestones
Received: 17 November 2015
Revised: 24 August 2017
Accepted: 28 September 2017
Published: 31 December 2017
Authors
David Helm
Department of Mathematics
Imperial College London
South Kensington Campus
London
United Kingdom
Yichao Tian
Mathematics Institute
University of Bonn
Bonn
Germany
Liang Xiao
Department of Mathematics
University of Connecticut
Storrs, CT
United States