{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:YDQYRNPKJBANY3R6OL6OJ325UE","short_pith_number":"pith:YDQYRNPK","schema_version":"1.0","canonical_sha256":"c0e188b5ea4840dc6e3e72fce4ef5da13118d2d19de40763165d6ad8ba1c6c84","source":{"kind":"arxiv","id":"1607.02044","version":2},"attestation_state":"computed","paper":{"title":"Proof of de Smit's conjecture: a freeness criterion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.NT"],"primary_cat":"math.AC","authors_text":"Sylvain Brochard","submitted_at":"2016-07-07T15:14:22Z","abstract_excerpt":"Let $A\\to B$ be a morphism of Artin local rings with the same embedding dimension. We prove that any $A$-flat $B$-module is $B$-flat. This freeness criterion was conjectured by de Smit in 1997 and improves Diamond's Theorem 2.1 from his 1997 paper \"The Taylor-Wiles construction and multiplicity one\". We also prove that if there is a nonzero $A$-flat $B$-module, then $A\\to B$ is flat and is a relative complete intersection (i.e. $B/\\mathfrak{m}_AB$ is a complete intersection). Then we explain how this result allows to simplify Wiles's proof of Fermat's Last Theorem: we do not need the so-called"},"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":"1607.02044","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-07-07T15:14:22Z","cross_cats_sorted":["math.AG","math.NT"],"title_canon_sha256":"e57468b18f718b8c20ccbd8f3d50510b7fb84138b663aca9c4c29fe27b14055d","abstract_canon_sha256":"cc50e193cb4f139cef620c3fa222ecdf9e474fe4c8f3e2adbba95c551c782927"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:13.090193Z","signature_b64":"xPRGsG6rTDLdQNbN79gnKJ8p85C3/tqOLUgbdxYd6R9WCZsWNanETsBo8uAGZ6WH61eoKk3VX+OTjvcKG2KWBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0e188b5ea4840dc6e3e72fce4ef5da13118d2d19de40763165d6ad8ba1c6c84","last_reissued_at":"2026-05-17T23:53:13.089636Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:13.089636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Proof of de Smit's conjecture: a freeness criterion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.NT"],"primary_cat":"math.AC","authors_text":"Sylvain Brochard","submitted_at":"2016-07-07T15:14:22Z","abstract_excerpt":"Let $A\\to B$ be a morphism of Artin local rings with the same embedding dimension. We prove that any $A$-flat $B$-module is $B$-flat. This freeness criterion was conjectured by de Smit in 1997 and improves Diamond's Theorem 2.1 from his 1997 paper \"The Taylor-Wiles construction and multiplicity one\". We also prove that if there is a nonzero $A$-flat $B$-module, then $A\\to B$ is flat and is a relative complete intersection (i.e. $B/\\mathfrak{m}_AB$ is a complete intersection). Then we explain how this result allows to simplify Wiles's proof of Fermat's Last Theorem: we do not need the so-called"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02044","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":"1607.02044","created_at":"2026-05-17T23:53:13.089730+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.02044v2","created_at":"2026-05-17T23:53:13.089730+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.02044","created_at":"2026-05-17T23:53:13.089730+00:00"},{"alias_kind":"pith_short_12","alias_value":"YDQYRNPKJBAN","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_16","alias_value":"YDQYRNPKJBANY3R6","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_8","alias_value":"YDQYRNPK","created_at":"2026-05-18T12:30:53.716459+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/YDQYRNPKJBANY3R6OL6OJ325UE","json":"https://pith.science/pith/YDQYRNPKJBANY3R6OL6OJ325UE.json","graph_json":"https://pith.science/api/pith-number/YDQYRNPKJBANY3R6OL6OJ325UE/graph.json","events_json":"https://pith.science/api/pith-number/YDQYRNPKJBANY3R6OL6OJ325UE/events.json","paper":"https://pith.science/paper/YDQYRNPK"},"agent_actions":{"view_html":"https://pith.science/pith/YDQYRNPKJBANY3R6OL6OJ325UE","download_json":"https://pith.science/pith/YDQYRNPKJBANY3R6OL6OJ325UE.json","view_paper":"https://pith.science/paper/YDQYRNPK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.02044&json=true","fetch_graph":"https://pith.science/api/pith-number/YDQYRNPKJBANY3R6OL6OJ325UE/graph.json","fetch_events":"https://pith.science/api/pith-number/YDQYRNPKJBANY3R6OL6OJ325UE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YDQYRNPKJBANY3R6OL6OJ325UE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YDQYRNPKJBANY3R6OL6OJ325UE/action/storage_attestation","attest_author":"https://pith.science/pith/YDQYRNPKJBANY3R6OL6OJ325UE/action/author_attestation","sign_citation":"https://pith.science/pith/YDQYRNPKJBANY3R6OL6OJ325UE/action/citation_signature","submit_replication":"https://pith.science/pith/YDQYRNPKJBANY3R6OL6OJ325UE/action/replication_record"}},"created_at":"2026-05-17T23:53:13.089730+00:00","updated_at":"2026-05-17T23:53:13.089730+00:00"}