{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:OSBGXH7YCFA4SNN43DI6FBL5DJ","short_pith_number":"pith:OSBGXH7Y","schema_version":"1.0","canonical_sha256":"74826b9ff81141c935bcd8d1e2857d1a51e150ce8fc22ce78e32ed10f92b55d2","source":{"kind":"arxiv","id":"1412.5300","version":2},"attestation_state":"computed","paper":{"title":"Rigid cohomology over Laurent series fields II: Finiteness and Poincar\\'e duality for smooth curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Ambrus P\\'al, Christopher Lazda","submitted_at":"2014-12-17T09:31:52Z","abstract_excerpt":"In this paper we prove that the $\\mathcal{E}^\\dagger_K$-valued cohomology, introduced in [9] is finite dimensional for smooth curves over Laurent series fields $k((t))$ in positive characteristic, and forms an $\\mathcal{E}^\\dagger_K$-lattice inside `classical' $\\mathcal{E}_K$-valued rigid cohomology. We do so by proving a suitable version of the p-adic local monodromy theory over $\\mathcal{E}^\\dagger_K$, and then using an \\'{e}tale pushforward for smooth curves to reduce to the case of $\\mathbb{A}^1$. We then introduce $\\mathcal{E}^\\dagger_K$-valued cohomology with compact supports, and again "},"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":"1412.5300","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-12-17T09:31:52Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"7140dadac30411a8bb48242b145a70dea3124bddec7fdbee959aacc621e53255","abstract_canon_sha256":"1e5e9b3d715b5bf88b769bf3516d6575009c3d95d8ce3cace116beff9ac5fab4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:04.505627Z","signature_b64":"Q388lRf1zr99h4foS4YlrkylLvra2e/49U+LwV1HQNqEfDLWW5hI/nkC31NEwDzsuB36lITs76ImDT6qA5r5Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74826b9ff81141c935bcd8d1e2857d1a51e150ce8fc22ce78e32ed10f92b55d2","last_reissued_at":"2026-05-18T02:25:04.505256Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:04.505256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rigid cohomology over Laurent series fields II: Finiteness and Poincar\\'e duality for smooth curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Ambrus P\\'al, Christopher Lazda","submitted_at":"2014-12-17T09:31:52Z","abstract_excerpt":"In this paper we prove that the $\\mathcal{E}^\\dagger_K$-valued cohomology, introduced in [9] is finite dimensional for smooth curves over Laurent series fields $k((t))$ in positive characteristic, and forms an $\\mathcal{E}^\\dagger_K$-lattice inside `classical' $\\mathcal{E}_K$-valued rigid cohomology. We do so by proving a suitable version of the p-adic local monodromy theory over $\\mathcal{E}^\\dagger_K$, and then using an \\'{e}tale pushforward for smooth curves to reduce to the case of $\\mathbb{A}^1$. We then introduce $\\mathcal{E}^\\dagger_K$-valued cohomology with compact supports, and again "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5300","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":"1412.5300","created_at":"2026-05-18T02:25:04.505310+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.5300v2","created_at":"2026-05-18T02:25:04.505310+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5300","created_at":"2026-05-18T02:25:04.505310+00:00"},{"alias_kind":"pith_short_12","alias_value":"OSBGXH7YCFA4","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_16","alias_value":"OSBGXH7YCFA4SNN4","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_8","alias_value":"OSBGXH7Y","created_at":"2026-05-18T12:28:43.426989+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/OSBGXH7YCFA4SNN43DI6FBL5DJ","json":"https://pith.science/pith/OSBGXH7YCFA4SNN43DI6FBL5DJ.json","graph_json":"https://pith.science/api/pith-number/OSBGXH7YCFA4SNN43DI6FBL5DJ/graph.json","events_json":"https://pith.science/api/pith-number/OSBGXH7YCFA4SNN43DI6FBL5DJ/events.json","paper":"https://pith.science/paper/OSBGXH7Y"},"agent_actions":{"view_html":"https://pith.science/pith/OSBGXH7YCFA4SNN43DI6FBL5DJ","download_json":"https://pith.science/pith/OSBGXH7YCFA4SNN43DI6FBL5DJ.json","view_paper":"https://pith.science/paper/OSBGXH7Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.5300&json=true","fetch_graph":"https://pith.science/api/pith-number/OSBGXH7YCFA4SNN43DI6FBL5DJ/graph.json","fetch_events":"https://pith.science/api/pith-number/OSBGXH7YCFA4SNN43DI6FBL5DJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OSBGXH7YCFA4SNN43DI6FBL5DJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OSBGXH7YCFA4SNN43DI6FBL5DJ/action/storage_attestation","attest_author":"https://pith.science/pith/OSBGXH7YCFA4SNN43DI6FBL5DJ/action/author_attestation","sign_citation":"https://pith.science/pith/OSBGXH7YCFA4SNN43DI6FBL5DJ/action/citation_signature","submit_replication":"https://pith.science/pith/OSBGXH7YCFA4SNN43DI6FBL5DJ/action/replication_record"}},"created_at":"2026-05-18T02:25:04.505310+00:00","updated_at":"2026-05-18T02:25:04.505310+00:00"}