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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"},"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":"1305.2874","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-05-13T17:50:34Z","cross_cats_sorted":[],"title_canon_sha256":"d72fadeba8a73e7fed16927bd38b10b81aa74ef4b82cfe86055571fd40a4572b","abstract_canon_sha256":"305d525e03d893018f9a5127d061620cab92ecf7c439b85c9e2791411fbfaea2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:26.282142Z","signature_b64":"MOKIwfuXKmR0iCvODCUGWTpt3iUCQQisbgE5TAzuy/BV6+fgWHO06ey4PbW6HrK9iOZinRCmUu6o5Gd4KTIHBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3c51729f7cc619fa68166b7e1e82260bd97e3e0b77cea8f65dfbd620bee2408","last_reissued_at":"2026-05-18T02:41:26.281705Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:26.281705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1305.2874","created_at":"2026-05-18T02:41:26.281761+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.2874v2","created_at":"2026-05-18T02:41:26.281761+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.2874","created_at":"2026-05-18T02:41:26.281761+00:00"},{"alias_kind":"pith_short_12","alias_value":"6PCROKPXZRQZ","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"6PCROKPXZRQZ7JUB","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"6PCROKPX","created_at":"2026-05-18T12:27:36.564083+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6PCROKPXZRQZ7JUBM236D2BCMC","json":"https://pith.science/pith/6PCROKPXZRQZ7JUBM236D2BCMC.json","graph_json":"https://pith.science/api/pith-number/6PCROKPXZRQZ7JUBM236D2BCMC/graph.json","events_json":"https://pith.science/api/pith-number/6PCROKPXZRQZ7JUBM236D2BCMC/events.json","paper":"https://pith.science/paper/6PCROKPX"},"agent_actions":{"view_html":"https://pith.science/pith/6PCROKPXZRQZ7JUBM236D2BCMC","download_json":"https://pith.science/pith/6PCROKPXZRQZ7JUBM236D2BCMC.json","view_paper":"https://pith.science/paper/6PCROKPX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.2874&json=true","fetch_graph":"https://pith.science/api/pith-number/6PCROKPXZRQZ7JUBM236D2BCMC/graph.json","fetch_events":"https://pith.science/api/pith-number/6PCROKPXZRQZ7JUBM236D2BCMC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6PCROKPXZRQZ7JUBM236D2BCMC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6PCROKPXZRQZ7JUBM236D2BCMC/action/storage_attestation","attest_author":"https://pith.science/pith/6PCROKPXZRQZ7JUBM236D2BCMC/action/author_attestation","sign_citation":"https://pith.science/pith/6PCROKPXZRQZ7JUBM236D2BCMC/action/citation_signature","submit_replication":"https://pith.science/pith/6PCROKPXZRQZ7JUBM236D2BCMC/action/replication_record"}},"created_at":"2026-05-18T02:41:26.281761+00:00","updated_at":"2026-05-18T02:41:26.281761+00:00"}