Vol. 11, No. 10, 2017

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

Volume 17
Issue 10, 1681–1865
Issue 9, 1533–1680
Issue 8, 1359–1532
Issue 7, 1239–1357
Issue 6, 1127–1237
Issue 5, 981–1126
Issue 4, 805–980
Issue 3, 541–804
Issue 2, 267–539
Issue 1, 1–266

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

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
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
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