{"paper":{"title":"On Tate conjecture for the special fibers of some unitary Shimura varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David Helm, Liang Xiao, Yichao Tian","submitted_at":"2014-10-09T03:11:12Z","abstract_excerpt":"Let $F$ be a totally real field in which a fixed prime $p$ is inert, and let $E$ be a CM extension of $F$ in which $p$ splits. We fix two positive integers $r,s \\in \\mathbb N$. We investigate the Tate conjecture on the special fiber of $G(U(r,s) \\times U(s,r))$-Shimura variety. We construct cycles which we conjecture to generate the Tate classes and verify our conjecture in the case of $G(U(1,s) \\times U(s,1))$. We also discuss the general conjecture regarding special cycles on the special fibers of unitary Shimura varieties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2343","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}