{"paper":{"title":"Algebraic cycles and Tate classes on Hilbert modular varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Heekyoung Hahn, Jayce R. Getz","submitted_at":"2015-07-16T00:34:51Z","abstract_excerpt":"Let $E/\\mathbb{Q}$ be a totally real number field that is Galois over $\\mathbb{Q}$, and let $\\pi$ be a cuspidal, nondihedral automorphic representation of $\\mathrm{GL}_2(\\mathbb{A}_E)$ that is in the lowest weight discrete series at every real place of $E$. The representation $\\pi$ cuts out a \"motive\" $M_\\mathrm{et}(\\pi^{\\infty})$ from the $\\ell$-adic middle degree intersection cohomology of an appropriate Hilbert modular variety. If $\\ell$ is sufficiently large in a sense that depends on $\\pi$ we compute the dimension of the space of Tate classes in $M_\\mathrm{et}(\\pi^{\\infty})$. Moreover if "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04422","kind":"arxiv","version":1},"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"}