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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1410.2343","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-10-09T03:11:12Z","cross_cats_sorted":[],"title_canon_sha256":"877f791b2f9e65e3336980d01e8a9acaf38cb116451bf4afd4bee11fd35a11e5","abstract_canon_sha256":"680c4c23b1c7c89cd857452cd512e4d91d9af663f2b07d255fdbd1c44e481d32"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:00.812207Z","signature_b64":"8gx3ee40DWLuKduKj95idDdRlrm2BiyhN8j5LCYkejvPvzC/B1fjCXpz1uXFq1VZ6nBbZoDIH6eAIxF/Lx1AAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"982237d5ddb5a635227bb33d05c984a4f68383a2440393e717fc10206d8dea96","last_reissued_at":"2026-05-18T00:21:00.811716Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:00.811716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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