{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:IVKX7M4XVCKRESU46GD6XWTQZ4","short_pith_number":"pith:IVKX7M4X","schema_version":"1.0","canonical_sha256":"45557fb397a895124a9cf187ebda70cf3b04b4e6de3734ba0cedcdb4847d542c","source":{"kind":"arxiv","id":"1806.00078","version":3},"attestation_state":"computed","paper":{"title":"Compactly generated t-structures in the derived category of a commutative ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AC","authors_text":"Michal Hrbek","submitted_at":"2018-05-31T20:22:16Z","abstract_excerpt":"We classify all compactly generated t-structures in the unbounded derived category of an arbitrary commutative ring, generalizing the result of [ATLJS10] for noetherian rings. More specifically, we establish a bijective correspondence between the compactly generated t-structures and infinite filtrations of the Zariski spectrum by Thomason subsets. Moreover, we show that in the case of a commutative noetherian ring, any bounded below homotopically smashing t-structure is compactly generated. As a consequence, all cosilting complexes are classified up to equivalence."},"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":"1806.00078","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-05-31T20:22:16Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"cb9bf7201357f9a353f097741c3cc5485be98a74518e7a121b6bd2038f481505","abstract_canon_sha256":"3ca9cc8c78af182e2b1c051dfccfdab93f28fab1701dee414903ddbc46637487"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:48.041773Z","signature_b64":"rEZZC7xk9icF9zhiiow0LDZXNL/hLtzTbZCHEk6v2/uLSOiQIK4IorispuPBIlxqSzHit0DxPUCR058ce4IQCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"45557fb397a895124a9cf187ebda70cf3b04b4e6de3734ba0cedcdb4847d542c","last_reissued_at":"2026-05-18T00:08:48.041046Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:48.041046Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Compactly generated t-structures in the derived category of a commutative ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AC","authors_text":"Michal Hrbek","submitted_at":"2018-05-31T20:22:16Z","abstract_excerpt":"We classify all compactly generated t-structures in the unbounded derived category of an arbitrary commutative ring, generalizing the result of [ATLJS10] for noetherian rings. More specifically, we establish a bijective correspondence between the compactly generated t-structures and infinite filtrations of the Zariski spectrum by Thomason subsets. Moreover, we show that in the case of a commutative noetherian ring, any bounded below homotopically smashing t-structure is compactly generated. As a consequence, all cosilting complexes are classified up to equivalence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00078","kind":"arxiv","version":3},"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":"1806.00078","created_at":"2026-05-18T00:08:48.041164+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.00078v3","created_at":"2026-05-18T00:08:48.041164+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.00078","created_at":"2026-05-18T00:08:48.041164+00:00"},{"alias_kind":"pith_short_12","alias_value":"IVKX7M4XVCKR","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_16","alias_value":"IVKX7M4XVCKRESU4","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_8","alias_value":"IVKX7M4X","created_at":"2026-05-18T12:32:31.084164+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/IVKX7M4XVCKRESU46GD6XWTQZ4","json":"https://pith.science/pith/IVKX7M4XVCKRESU46GD6XWTQZ4.json","graph_json":"https://pith.science/api/pith-number/IVKX7M4XVCKRESU46GD6XWTQZ4/graph.json","events_json":"https://pith.science/api/pith-number/IVKX7M4XVCKRESU46GD6XWTQZ4/events.json","paper":"https://pith.science/paper/IVKX7M4X"},"agent_actions":{"view_html":"https://pith.science/pith/IVKX7M4XVCKRESU46GD6XWTQZ4","download_json":"https://pith.science/pith/IVKX7M4XVCKRESU46GD6XWTQZ4.json","view_paper":"https://pith.science/paper/IVKX7M4X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.00078&json=true","fetch_graph":"https://pith.science/api/pith-number/IVKX7M4XVCKRESU46GD6XWTQZ4/graph.json","fetch_events":"https://pith.science/api/pith-number/IVKX7M4XVCKRESU46GD6XWTQZ4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IVKX7M4XVCKRESU46GD6XWTQZ4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IVKX7M4XVCKRESU46GD6XWTQZ4/action/storage_attestation","attest_author":"https://pith.science/pith/IVKX7M4XVCKRESU46GD6XWTQZ4/action/author_attestation","sign_citation":"https://pith.science/pith/IVKX7M4XVCKRESU46GD6XWTQZ4/action/citation_signature","submit_replication":"https://pith.science/pith/IVKX7M4XVCKRESU46GD6XWTQZ4/action/replication_record"}},"created_at":"2026-05-18T00:08:48.041164+00:00","updated_at":"2026-05-18T00:08:48.041164+00:00"}