{"paper":{"title":"Comments on Sampson's approach toward Hodge conjecture on Abelian varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Tuyen Trung Truong","submitted_at":"2014-09-01T17:45:54Z","abstract_excerpt":"Let $A$ be an Abelian variety of dimension $n$. For $0<p<2n$ an odd integer, Sampson constructed a surjective homomorphism $\\pi :J^p(A)\\rightarrow A$, where $J^p(A)$ is the higher Weil Jacobian variety of $A$. Let $\\widehat{\\omega}$ be a fixed form in $H^{1,1}(J^p(A),\\mathbb{Q})$, and $N=\\dim (J^p(A))$. He observes that if the map $\\pi _*(\\widehat{\\omega }^{N-p-1}\\wedge .): H^{1,1}(J^p(A),\\mathbb{Q})\\rightarrow H^{n-p,n-p}(A,\\mathbb{Q})$ is injective, then the Hodge conjecture is true for $A$ in bidegree $(p,p)$.\n  In this paper, we give some clarification of the approach and show that the map"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0495","kind":"arxiv","version":3},"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"}