{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:WPOLFQFFM6T2JUB24VKRXPLRW2","short_pith_number":"pith:WPOLFQFF","schema_version":"1.0","canonical_sha256":"b3dcb2c0a567a7a4d03ae5551bbd71b6b06565eb454092f65cc88864d2d7006a","source":{"kind":"arxiv","id":"1602.06899","version":3},"attestation_state":"computed","paper":{"title":"Relative p-adic Hodge theory, II: Imperfect period rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Kiran S. Kedlaya, Ruochuan Liu","submitted_at":"2016-02-22T19:26:50Z","abstract_excerpt":"In a previous paper, we constructed a category of (phi, Gamma)-modules associated to any adic space over Q_p with the property that the etale (phi, Gamma)-modules correspond to etale Q_p-local systems; these involve sheaves of period rings for Scholze's pro-etale topology. In this paper, we first extend Kiehl's theory of coherent sheaves on rigid analytic spaces to a theory of pseudocoherent sheaves on adic spaces, then construct a corresponding theory of pseudocoherent (phi, Gamma)-modules. We then relate these objects to a more explicit construction in case the space comes equipped with a su"},"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":"1602.06899","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-22T19:26:50Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"a183bcec43e1a81ddc2ec543084400697dfacffd98e6fbc6487a8c717aac6bfe","abstract_canon_sha256":"e6fcd069c528e2148eb6a41d021a6595f057232aabbaba1c1bc97a3967a49f5a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:13:27.921278Z","signature_b64":"b61g6KdmwdYNJ2GBSxXLA6nXlvYhH/MKw0a8S9QN832z4gDghQmsvW8VKY9b7Omf79TV9EOsCEu91Lfw7jb9Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3dcb2c0a567a7a4d03ae5551bbd71b6b06565eb454092f65cc88864d2d7006a","last_reissued_at":"2026-07-05T00:13:27.920850Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:13:27.920850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Relative p-adic Hodge theory, II: Imperfect period rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Kiran S. Kedlaya, Ruochuan Liu","submitted_at":"2016-02-22T19:26:50Z","abstract_excerpt":"In a previous paper, we constructed a category of (phi, Gamma)-modules associated to any adic space over Q_p with the property that the etale (phi, Gamma)-modules correspond to etale Q_p-local systems; these involve sheaves of period rings for Scholze's pro-etale topology. In this paper, we first extend Kiehl's theory of coherent sheaves on rigid analytic spaces to a theory of pseudocoherent sheaves on adic spaces, then construct a corresponding theory of pseudocoherent (phi, Gamma)-modules. We then relate these objects to a more explicit construction in case the space comes equipped with a su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06899","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1602.06899/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1602.06899","created_at":"2026-07-05T00:13:27.920914+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.06899v3","created_at":"2026-07-05T00:13:27.920914+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.06899","created_at":"2026-07-05T00:13:27.920914+00:00"},{"alias_kind":"pith_short_12","alias_value":"WPOLFQFFM6T2","created_at":"2026-07-05T00:13:27.920914+00:00"},{"alias_kind":"pith_short_16","alias_value":"WPOLFQFFM6T2JUB2","created_at":"2026-07-05T00:13:27.920914+00:00"},{"alias_kind":"pith_short_8","alias_value":"WPOLFQFF","created_at":"2026-07-05T00:13:27.920914+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":7,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.28818","citing_title":"To be or not to be local","ref_index":23,"is_internal_anchor":false},{"citing_arxiv_id":"2606.23600","citing_title":"Virtual Surjection and the $n$-$(n+1)$-$(n+2)$ Theorem for Profinite Groups","ref_index":7,"is_internal_anchor":false},{"citing_arxiv_id":"2207.07623","citing_title":"$G$-torsors on perfectoid spaces","ref_index":19,"is_internal_anchor":false},{"citing_arxiv_id":"2512.21418","citing_title":"A $p$-adic Simpson correspondence for singular rigid-analytic varieties","ref_index":35,"is_internal_anchor":false},{"citing_arxiv_id":"2604.03220","citing_title":"p-adic Hodge theory of de Rham local systems, I: Newton polygon and monodromy","ref_index":14,"is_internal_anchor":false},{"citing_arxiv_id":"2605.03655","citing_title":"Lectures on Analytic Geometry","ref_index":26,"is_internal_anchor":false},{"citing_arxiv_id":"2604.17799","citing_title":"Semistable Reduction Theorem for Overconvergent $F$-isocrystals over Laurent Series Fields","ref_index":21,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WPOLFQFFM6T2JUB24VKRXPLRW2","json":"https://pith.science/pith/WPOLFQFFM6T2JUB24VKRXPLRW2.json","graph_json":"https://pith.science/api/pith-number/WPOLFQFFM6T2JUB24VKRXPLRW2/graph.json","events_json":"https://pith.science/api/pith-number/WPOLFQFFM6T2JUB24VKRXPLRW2/events.json","paper":"https://pith.science/paper/WPOLFQFF"},"agent_actions":{"view_html":"https://pith.science/pith/WPOLFQFFM6T2JUB24VKRXPLRW2","download_json":"https://pith.science/pith/WPOLFQFFM6T2JUB24VKRXPLRW2.json","view_paper":"https://pith.science/paper/WPOLFQFF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.06899&json=true","fetch_graph":"https://pith.science/api/pith-number/WPOLFQFFM6T2JUB24VKRXPLRW2/graph.json","fetch_events":"https://pith.science/api/pith-number/WPOLFQFFM6T2JUB24VKRXPLRW2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WPOLFQFFM6T2JUB24VKRXPLRW2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WPOLFQFFM6T2JUB24VKRXPLRW2/action/storage_attestation","attest_author":"https://pith.science/pith/WPOLFQFFM6T2JUB24VKRXPLRW2/action/author_attestation","sign_citation":"https://pith.science/pith/WPOLFQFFM6T2JUB24VKRXPLRW2/action/citation_signature","submit_replication":"https://pith.science/pith/WPOLFQFFM6T2JUB24VKRXPLRW2/action/replication_record"}},"created_at":"2026-07-05T00:13:27.920914+00:00","updated_at":"2026-07-05T00:13:27.920914+00:00"}