{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:DTPNL2L5JKFIWPKXHZJLJZQJ3E","short_pith_number":"pith:DTPNL2L5","schema_version":"1.0","canonical_sha256":"1cded5e97d4a8a8b3d573e52b4e609d921df40e712af3708508960acee3f5420","source":{"kind":"arxiv","id":"1212.4544","version":4},"attestation_state":"computed","paper":{"title":"The quot functor of a quasi-coherent sheaf","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AG","authors_text":"Gennaro di Brino","submitted_at":"2012-12-19T00:39:13Z","abstract_excerpt":"We build an infinite dimensional scheme parametrizing isomorphism classes of coherent quotients of a quasi-coherent sheaf on a projective scheme. The main tool to achieve the construction is a version of Grothendieck's Grassmannian embedding combined with a result of Deligne, realizing quasi-coherent sheaves as ind-objects in the category of quasi-coherent sheaves of finite presentation. We end our treatment with the discussion of a special case in which we can retain an analog of the Grassmannian embedding."},"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":"1212.4544","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-12-19T00:39:13Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"672c03086bf26a2d5fc9806d4a89aaeb47bc043036b1da1028c83b311a0a771d","abstract_canon_sha256":"aaa78331b752c2964844dccb1f4fc13785ca157aec478ad71dda6f493f07b9c8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:10.406561Z","signature_b64":"0p/BL/DhG3a+AoU8kTGZmqGGXZg3UOLbG0CY34H4IMXtoiKoXLyYm/CO1BTmtnU9vHRBqQoEwh8DCxtBki8WCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cded5e97d4a8a8b3d573e52b4e609d921df40e712af3708508960acee3f5420","last_reissued_at":"2026-05-18T00:44:10.405930Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:10.405930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The quot functor of a quasi-coherent sheaf","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AG","authors_text":"Gennaro di Brino","submitted_at":"2012-12-19T00:39:13Z","abstract_excerpt":"We build an infinite dimensional scheme parametrizing isomorphism classes of coherent quotients of a quasi-coherent sheaf on a projective scheme. The main tool to achieve the construction is a version of Grothendieck's Grassmannian embedding combined with a result of Deligne, realizing quasi-coherent sheaves as ind-objects in the category of quasi-coherent sheaves of finite presentation. We end our treatment with the discussion of a special case in which we can retain an analog of the Grassmannian embedding."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4544","kind":"arxiv","version":4},"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":"1212.4544","created_at":"2026-05-18T00:44:10.406016+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.4544v4","created_at":"2026-05-18T00:44:10.406016+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4544","created_at":"2026-05-18T00:44:10.406016+00:00"},{"alias_kind":"pith_short_12","alias_value":"DTPNL2L5JKFI","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_16","alias_value":"DTPNL2L5JKFIWPKX","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_8","alias_value":"DTPNL2L5","created_at":"2026-05-18T12:27:04.183437+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/DTPNL2L5JKFIWPKXHZJLJZQJ3E","json":"https://pith.science/pith/DTPNL2L5JKFIWPKXHZJLJZQJ3E.json","graph_json":"https://pith.science/api/pith-number/DTPNL2L5JKFIWPKXHZJLJZQJ3E/graph.json","events_json":"https://pith.science/api/pith-number/DTPNL2L5JKFIWPKXHZJLJZQJ3E/events.json","paper":"https://pith.science/paper/DTPNL2L5"},"agent_actions":{"view_html":"https://pith.science/pith/DTPNL2L5JKFIWPKXHZJLJZQJ3E","download_json":"https://pith.science/pith/DTPNL2L5JKFIWPKXHZJLJZQJ3E.json","view_paper":"https://pith.science/paper/DTPNL2L5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.4544&json=true","fetch_graph":"https://pith.science/api/pith-number/DTPNL2L5JKFIWPKXHZJLJZQJ3E/graph.json","fetch_events":"https://pith.science/api/pith-number/DTPNL2L5JKFIWPKXHZJLJZQJ3E/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DTPNL2L5JKFIWPKXHZJLJZQJ3E/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DTPNL2L5JKFIWPKXHZJLJZQJ3E/action/storage_attestation","attest_author":"https://pith.science/pith/DTPNL2L5JKFIWPKXHZJLJZQJ3E/action/author_attestation","sign_citation":"https://pith.science/pith/DTPNL2L5JKFIWPKXHZJLJZQJ3E/action/citation_signature","submit_replication":"https://pith.science/pith/DTPNL2L5JKFIWPKXHZJLJZQJ3E/action/replication_record"}},"created_at":"2026-05-18T00:44:10.406016+00:00","updated_at":"2026-05-18T00:44:10.406016+00:00"}