{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:XAYDQ2XZMQYS57F3GWF4XXCG5P","short_pith_number":"pith:XAYDQ2XZ","schema_version":"1.0","canonical_sha256":"b830386af964312efcbb358bcbdc46ebe110248451356351aa128de36ac3d26c","source":{"kind":"arxiv","id":"1207.6193","version":1},"attestation_state":"computed","paper":{"title":"Completions and derived de Rham cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Bhargav Bhatt","submitted_at":"2012-07-26T07:58:52Z","abstract_excerpt":"We show that Illusie's derived de Rham cohomology (Hodge-completed) coincides with Hartshorne's algebraic de Rham cohomology for a finite type map of noetherian schemes in characteristic 0; the case of lci morphisms was a result of Illusie. In particular, the E_1-differentials in the derived Hodge-to-de Rham spectral sequence for singular varieties are often non-zero. Another consequence is a completely elementary description of Hartshorne's algebraic de Rham cohomology: it is computed by the completed Amitsur complex for any variety in characteristic 0."},"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":"1207.6193","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-07-26T07:58:52Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"af9486eca64bbef4603a9b09652f8426aa0000fdf2c2246f0609a2f3f4ae44b5","abstract_canon_sha256":"a10ab2c7609c1035c7580384fe378f44549abdbd3b6c62b76b6d9cc077b59a9f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:08.556721Z","signature_b64":"wOjx31u4qoGc9HFw6Px22k+KWZACk+RT3PNugKUFtyF1Fj9r7y5CfEbW59fCJ+EDDZfWxOGDUsCCybGHJejSBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b830386af964312efcbb358bcbdc46ebe110248451356351aa128de36ac3d26c","last_reissued_at":"2026-05-18T03:50:08.555943Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:08.555943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Completions and derived de Rham cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Bhargav Bhatt","submitted_at":"2012-07-26T07:58:52Z","abstract_excerpt":"We show that Illusie's derived de Rham cohomology (Hodge-completed) coincides with Hartshorne's algebraic de Rham cohomology for a finite type map of noetherian schemes in characteristic 0; the case of lci morphisms was a result of Illusie. In particular, the E_1-differentials in the derived Hodge-to-de Rham spectral sequence for singular varieties are often non-zero. Another consequence is a completely elementary description of Hartshorne's algebraic de Rham cohomology: it is computed by the completed Amitsur complex for any variety in characteristic 0."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6193","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1207.6193","created_at":"2026-05-18T03:50:08.556075+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.6193v1","created_at":"2026-05-18T03:50:08.556075+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6193","created_at":"2026-05-18T03:50:08.556075+00:00"},{"alias_kind":"pith_short_12","alias_value":"XAYDQ2XZMQYS","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_16","alias_value":"XAYDQ2XZMQYS57F3","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_8","alias_value":"XAYDQ2XZ","created_at":"2026-05-18T12:27:27.928770+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2208.01517","citing_title":"Derived $F$-zips","ref_index":4,"is_internal_anchor":true},{"citing_arxiv_id":"2312.13129","citing_title":"Logarithmic prismatic cohomology, motivic sheaves, and comparison theorems","ref_index":4,"is_internal_anchor":true},{"citing_arxiv_id":"2604.20005","citing_title":"$F$-finite schemes have a dualizing complex","ref_index":6,"is_internal_anchor":false},{"citing_arxiv_id":"2604.05825","citing_title":"Hodge-to-de Rham degeneration and quasihomogeneous singularities of curves","ref_index":1,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XAYDQ2XZMQYS57F3GWF4XXCG5P","json":"https://pith.science/pith/XAYDQ2XZMQYS57F3GWF4XXCG5P.json","graph_json":"https://pith.science/api/pith-number/XAYDQ2XZMQYS57F3GWF4XXCG5P/graph.json","events_json":"https://pith.science/api/pith-number/XAYDQ2XZMQYS57F3GWF4XXCG5P/events.json","paper":"https://pith.science/paper/XAYDQ2XZ"},"agent_actions":{"view_html":"https://pith.science/pith/XAYDQ2XZMQYS57F3GWF4XXCG5P","download_json":"https://pith.science/pith/XAYDQ2XZMQYS57F3GWF4XXCG5P.json","view_paper":"https://pith.science/paper/XAYDQ2XZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.6193&json=true","fetch_graph":"https://pith.science/api/pith-number/XAYDQ2XZMQYS57F3GWF4XXCG5P/graph.json","fetch_events":"https://pith.science/api/pith-number/XAYDQ2XZMQYS57F3GWF4XXCG5P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XAYDQ2XZMQYS57F3GWF4XXCG5P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XAYDQ2XZMQYS57F3GWF4XXCG5P/action/storage_attestation","attest_author":"https://pith.science/pith/XAYDQ2XZMQYS57F3GWF4XXCG5P/action/author_attestation","sign_citation":"https://pith.science/pith/XAYDQ2XZMQYS57F3GWF4XXCG5P/action/citation_signature","submit_replication":"https://pith.science/pith/XAYDQ2XZMQYS57F3GWF4XXCG5P/action/replication_record"}},"created_at":"2026-05-18T03:50:08.556075+00:00","updated_at":"2026-05-18T03:50:08.556075+00:00"}