{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EE2I3BZCN3YHICJMB2IKH4AXBN","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8d2cfce663893c4301d4db8994fd7796ba3aad4614f8775d0ff1c3bbfa01b03e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-07-25T20:57:02Z","title_canon_sha256":"927000acaebc146a984869b7fe8bb0aa43ddbe337e26d34b398c66eb794d2977"},"schema_version":"1.0","source":{"id":"1807.09854","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.09854","created_at":"2026-05-17T23:58:13Z"},{"alias_kind":"arxiv_version","alias_value":"1807.09854v2","created_at":"2026-05-17T23:58:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.09854","created_at":"2026-05-17T23:58:13Z"},{"alias_kind":"pith_short_12","alias_value":"EE2I3BZCN3YH","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EE2I3BZCN3YHICJM","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EE2I3BZC","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:4e5ed6ab4897aa110648236dd4429ec08ca7dadfafdcd084508572099f08ef11","target":"graph","created_at":"2026-05-17T23:58:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $a_X:X\\rightarrow \\mathrm{Alb}\\, X$ be the Albanese map of a smooth complex projective variety. Roughly speaking in this note we prove that for all $i \\geq 0$ and $\\alpha\\in \\mathrm{Pic}^0\\, X$, the cohomology ranks $h^i(\\mathrm{Alb}\\, X, \\,{a_X}_* \\omega_X\\otimes P_\\alpha)$ are derived invariants. In the case of varieties of maximal Albanese dimension this proves conjectures of Popa and Lombardi-Popa -including the derived invariance of the Hodge numbers $h^{0,j}$ -- and a weaker version of them for arbitrary varieties. Finally we provide an application to derived invariance of certain ir","authors_text":"Federico Caucci, Giuseppe Pareschi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-07-25T20:57:02Z","title":"Derived invariants arising from the Albanese map"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.09854","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:448ed44fc1616ec29ce1f7363d344ea390083e5d642af9a7eb950da8a0e7c6cc","target":"record","created_at":"2026-05-17T23:58:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8d2cfce663893c4301d4db8994fd7796ba3aad4614f8775d0ff1c3bbfa01b03e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-07-25T20:57:02Z","title_canon_sha256":"927000acaebc146a984869b7fe8bb0aa43ddbe337e26d34b398c66eb794d2977"},"schema_version":"1.0","source":{"id":"1807.09854","kind":"arxiv","version":2}},"canonical_sha256":"21348d87226ef074092c0e90a3f0170b7dd8f4f2a27ae31e82939bce100f37f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21348d87226ef074092c0e90a3f0170b7dd8f4f2a27ae31e82939bce100f37f6","first_computed_at":"2026-05-17T23:58:13.996233Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:13.996233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DnrohhDyWEbFDNXQchMZOaU9eloI4VIy/410PX/ibqyRu9O4PwHcQ0lPH1yzdeQqKp0pg1kchwHP+NPCjL3HAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:13.996810Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.09854","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:448ed44fc1616ec29ce1f7363d344ea390083e5d642af9a7eb950da8a0e7c6cc","sha256:4e5ed6ab4897aa110648236dd4429ec08ca7dadfafdcd084508572099f08ef11"],"state_sha256":"7d022796ccd9959f37c80c21a38002b99ea3268bd7d9bbaa9b3095343ea207fb"}