{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:7BQTI6SALZAR2SLASPQZSSKDM7","short_pith_number":"pith:7BQTI6SA","schema_version":"1.0","canonical_sha256":"f861347a405e411d496093e199494367d0f9207610dc866dcd51f9433594d6d7","source":{"kind":"arxiv","id":"1602.09016","version":5},"attestation_state":"computed","paper":{"title":"Some ring-theoretic properties of A_inf","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kiran S. Kedlaya","submitted_at":"2016-02-29T15:57:45Z","abstract_excerpt":"The ring of Witt vectors over a perfect valuation ring of characteristic p, often denoted A_inf, plays a pivotal role in p-adic Hodge theory; for instance, Bhatt, Morrow, and Scholze have recently reinterpreted and refined the crystalline comparison isomorphism by relating it to a certain A_inf-valued cohomology theory. We address some basic ring-theoretic questions about A_inf motivated by analogies with two-dimensional regular local rings. For example, we show that in most cases A_inf, which is manifestly not noetherian, is also not coherent. On the other hand, it does have the property that"},"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":"1602.09016","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-29T15:57:45Z","cross_cats_sorted":[],"title_canon_sha256":"143b1af5b8bcff30b757f682485096314f15a56c2f163846d38b33980244563f","abstract_canon_sha256":"0d17c09532466f8dd33435840009c732e72316727363688e0b846037605776f9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:43.595861Z","signature_b64":"O9BuFVHmOpccXrXWG7HinY/esPmUIL4+UAhGRDBjvh50Fx6Ji9CRpspvigbBQZs/F8Vs2YZElj9jTyCfhqrOCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f861347a405e411d496093e199494367d0f9207610dc866dcd51f9433594d6d7","last_reissued_at":"2026-05-17T23:43:43.595185Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:43.595185Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some ring-theoretic properties of A_inf","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kiran S. Kedlaya","submitted_at":"2016-02-29T15:57:45Z","abstract_excerpt":"The ring of Witt vectors over a perfect valuation ring of characteristic p, often denoted A_inf, plays a pivotal role in p-adic Hodge theory; for instance, Bhatt, Morrow, and Scholze have recently reinterpreted and refined the crystalline comparison isomorphism by relating it to a certain A_inf-valued cohomology theory. We address some basic ring-theoretic questions about A_inf motivated by analogies with two-dimensional regular local rings. For example, we show that in most cases A_inf, which is manifestly not noetherian, is also not coherent. On the other hand, it does have the property that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.09016","kind":"arxiv","version":5},"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":"1602.09016","created_at":"2026-05-17T23:43:43.595297+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.09016v5","created_at":"2026-05-17T23:43:43.595297+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.09016","created_at":"2026-05-17T23:43:43.595297+00:00"},{"alias_kind":"pith_short_12","alias_value":"7BQTI6SALZAR","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_16","alias_value":"7BQTI6SALZAR2SLA","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_8","alias_value":"7BQTI6SA","created_at":"2026-05-18T12:30:04.600751+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/7BQTI6SALZAR2SLASPQZSSKDM7","json":"https://pith.science/pith/7BQTI6SALZAR2SLASPQZSSKDM7.json","graph_json":"https://pith.science/api/pith-number/7BQTI6SALZAR2SLASPQZSSKDM7/graph.json","events_json":"https://pith.science/api/pith-number/7BQTI6SALZAR2SLASPQZSSKDM7/events.json","paper":"https://pith.science/paper/7BQTI6SA"},"agent_actions":{"view_html":"https://pith.science/pith/7BQTI6SALZAR2SLASPQZSSKDM7","download_json":"https://pith.science/pith/7BQTI6SALZAR2SLASPQZSSKDM7.json","view_paper":"https://pith.science/paper/7BQTI6SA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.09016&json=true","fetch_graph":"https://pith.science/api/pith-number/7BQTI6SALZAR2SLASPQZSSKDM7/graph.json","fetch_events":"https://pith.science/api/pith-number/7BQTI6SALZAR2SLASPQZSSKDM7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7BQTI6SALZAR2SLASPQZSSKDM7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7BQTI6SALZAR2SLASPQZSSKDM7/action/storage_attestation","attest_author":"https://pith.science/pith/7BQTI6SALZAR2SLASPQZSSKDM7/action/author_attestation","sign_citation":"https://pith.science/pith/7BQTI6SALZAR2SLASPQZSSKDM7/action/citation_signature","submit_replication":"https://pith.science/pith/7BQTI6SALZAR2SLASPQZSSKDM7/action/replication_record"}},"created_at":"2026-05-17T23:43:43.595297+00:00","updated_at":"2026-05-17T23:43:43.595297+00:00"}