{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:ZMJPTQ2WJSXLTU6QG42VH6RVQL","short_pith_number":"pith:ZMJPTQ2W","schema_version":"1.0","canonical_sha256":"cb12f9c3564caeb9d3d0373553fa3582fbe0456f7b18a8cb43fe4ffc0fa9372f","source":{"kind":"arxiv","id":"1009.2668","version":2},"attestation_state":"computed","paper":{"title":"Some properties and applications of $F$-finite $F$-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Mordechai Katzman","submitted_at":"2010-09-14T13:54:57Z","abstract_excerpt":"The purpose of this paper is to describe several applications of finiteness properties of $F$-finite $F$-modules recently discovered by M. Hochster to the study of Frobenius maps on injective hulls, Frobenius near-splittings and to the nature of morphisms of $F$-finite $F$-modules.\n  Among the results in the paper we show that morphisms of $F$-finite $F$-modules have a particularly simple form, and we show that certain Frobenius near-splittings have finitely many compatible submodules, thus generalizing a result of M. Blickle and G. B\\\"ockle to the non-$F$-finite case."},"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":"1009.2668","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-09-14T13:54:57Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"0edf959f44fba9dba59c70a0a5046a0c87e63bc6dd5b2efe34f1e0d7142bccd2","abstract_canon_sha256":"79ba592224aede1905d9d29da54c0de5ecde697677329df5799f5aa504bfb20e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:04.550662Z","signature_b64":"pNwLsRcgS5aOaUaFD/SBxd/DoSglxr9PaU896mGaG94lFw+nPnfRyIUomSA9W5bBX3KwufZszduuKJ6C6QCIDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb12f9c3564caeb9d3d0373553fa3582fbe0456f7b18a8cb43fe4ffc0fa9372f","last_reissued_at":"2026-05-18T04:30:04.550244Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:04.550244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some properties and applications of $F$-finite $F$-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Mordechai Katzman","submitted_at":"2010-09-14T13:54:57Z","abstract_excerpt":"The purpose of this paper is to describe several applications of finiteness properties of $F$-finite $F$-modules recently discovered by M. Hochster to the study of Frobenius maps on injective hulls, Frobenius near-splittings and to the nature of morphisms of $F$-finite $F$-modules.\n  Among the results in the paper we show that morphisms of $F$-finite $F$-modules have a particularly simple form, and we show that certain Frobenius near-splittings have finitely many compatible submodules, thus generalizing a result of M. Blickle and G. B\\\"ockle to the non-$F$-finite case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2668","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":"1009.2668","created_at":"2026-05-18T04:30:04.550296+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.2668v2","created_at":"2026-05-18T04:30:04.550296+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2668","created_at":"2026-05-18T04:30:04.550296+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZMJPTQ2WJSXL","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZMJPTQ2WJSXLTU6Q","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZMJPTQ2W","created_at":"2026-05-18T12:26:18.847500+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/ZMJPTQ2WJSXLTU6QG42VH6RVQL","json":"https://pith.science/pith/ZMJPTQ2WJSXLTU6QG42VH6RVQL.json","graph_json":"https://pith.science/api/pith-number/ZMJPTQ2WJSXLTU6QG42VH6RVQL/graph.json","events_json":"https://pith.science/api/pith-number/ZMJPTQ2WJSXLTU6QG42VH6RVQL/events.json","paper":"https://pith.science/paper/ZMJPTQ2W"},"agent_actions":{"view_html":"https://pith.science/pith/ZMJPTQ2WJSXLTU6QG42VH6RVQL","download_json":"https://pith.science/pith/ZMJPTQ2WJSXLTU6QG42VH6RVQL.json","view_paper":"https://pith.science/paper/ZMJPTQ2W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.2668&json=true","fetch_graph":"https://pith.science/api/pith-number/ZMJPTQ2WJSXLTU6QG42VH6RVQL/graph.json","fetch_events":"https://pith.science/api/pith-number/ZMJPTQ2WJSXLTU6QG42VH6RVQL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZMJPTQ2WJSXLTU6QG42VH6RVQL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZMJPTQ2WJSXLTU6QG42VH6RVQL/action/storage_attestation","attest_author":"https://pith.science/pith/ZMJPTQ2WJSXLTU6QG42VH6RVQL/action/author_attestation","sign_citation":"https://pith.science/pith/ZMJPTQ2WJSXLTU6QG42VH6RVQL/action/citation_signature","submit_replication":"https://pith.science/pith/ZMJPTQ2WJSXLTU6QG42VH6RVQL/action/replication_record"}},"created_at":"2026-05-18T04:30:04.550296+00:00","updated_at":"2026-05-18T04:30:04.550296+00:00"}