{"paper":{"title":"Decomposition de motifs abeliens","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Giuseppe Ancona","submitted_at":"2013-05-13T17:50:34Z","abstract_excerpt":"Let A be an abelian variety and let us fix a Weil cohomology with coefficients in F. Let $H^1(A,F)$ be the first cohomology group of A and $Lef(A) \\subset GL(H^1(A,F))$ be its Lefschetz group, i.e. the sub-group of $GL(H^1(A,F))$ of linear applications commuting with endomorphisms of A and respecting the pairing induced by a polarization. We give an explicit presentation of a $\\mathbb{Q}$-algebra of correspondences $B_{i,r}$ such that the cycle class map induces an isomorphism $cl_{|_{B_{i,r}}}: B_{i,r} \\otimes_{\\mathbb{Q}} F \\cong End_{Lef(A)}(H^i(A^r,F)).$ We also give relative versions of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2874","kind":"arxiv","version":2},"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"}