{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:PNJZM3QRPUV4A2ZG7Z7BPPKEQN","short_pith_number":"pith:PNJZM3QR","schema_version":"1.0","canonical_sha256":"7b53966e117d2bc06b26fe7e17bd44834d536bb45c9febcb3b9277684b450b3b","source":{"kind":"arxiv","id":"1304.5376","version":3},"attestation_state":"computed","paper":{"title":"Calculabilit\\'e de la cohomologie \\'etale modulo l","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"David A. Madore, Fabrice Orgogozo","submitted_at":"2013-04-19T11:28:34Z","abstract_excerpt":"Let $X$ be an algebraic scheme over an algebraically closed field and $\\ell$ a prime number invertible on $X$. According to classical results (due essentially to A. Grothendieck, M. Artin and P. Deligne), the \\'etale cohomology groups $\\mathrm{H}^i(X,\\mathbb{Z}/\\ell\\mathbb{Z})$ are finite-dimensional. Using an $\\ell$-adic variant of M. Artin's good neighborhoods and elementary results on the cohomology of pro-$\\ell$ groups, we express the cohomology of $X$ as a well controlled colimit of that of toposes constructed on $BG$ where the $G$ are computable finite $\\ell$-groups. From this, we deduce"},"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":"1304.5376","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-04-19T11:28:34Z","cross_cats_sorted":[],"title_canon_sha256":"b33ccecda8c11676ed07f89bbfd8aaca898b3aa03376e5f11e46ef66b40c33f2","abstract_canon_sha256":"676cf51450b8f7e86a513da51967e621649b56ff186ec240c14a05a66ccbaea4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:25.455495Z","signature_b64":"zDe/V23/IXvsp4kmX2jJOuaHEayBbQvHtu/jxGvHdjOXsYW1P6pJ3/VdHojGXjYc4DQpwkAC+rWvCRY4o4PIDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b53966e117d2bc06b26fe7e17bd44834d536bb45c9febcb3b9277684b450b3b","last_reissued_at":"2026-05-18T01:22:25.454847Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:25.454847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Calculabilit\\'e de la cohomologie \\'etale modulo l","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"David A. Madore, Fabrice Orgogozo","submitted_at":"2013-04-19T11:28:34Z","abstract_excerpt":"Let $X$ be an algebraic scheme over an algebraically closed field and $\\ell$ a prime number invertible on $X$. According to classical results (due essentially to A. Grothendieck, M. Artin and P. Deligne), the \\'etale cohomology groups $\\mathrm{H}^i(X,\\mathbb{Z}/\\ell\\mathbb{Z})$ are finite-dimensional. Using an $\\ell$-adic variant of M. Artin's good neighborhoods and elementary results on the cohomology of pro-$\\ell$ groups, we express the cohomology of $X$ as a well controlled colimit of that of toposes constructed on $BG$ where the $G$ are computable finite $\\ell$-groups. From this, we deduce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5376","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":""},"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":"1304.5376","created_at":"2026-05-18T01:22:25.454968+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.5376v3","created_at":"2026-05-18T01:22:25.454968+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5376","created_at":"2026-05-18T01:22:25.454968+00:00"},{"alias_kind":"pith_short_12","alias_value":"PNJZM3QRPUV4","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"PNJZM3QRPUV4A2ZG","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"PNJZM3QR","created_at":"2026-05-18T12:27:54.935989+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/PNJZM3QRPUV4A2ZG7Z7BPPKEQN","json":"https://pith.science/pith/PNJZM3QRPUV4A2ZG7Z7BPPKEQN.json","graph_json":"https://pith.science/api/pith-number/PNJZM3QRPUV4A2ZG7Z7BPPKEQN/graph.json","events_json":"https://pith.science/api/pith-number/PNJZM3QRPUV4A2ZG7Z7BPPKEQN/events.json","paper":"https://pith.science/paper/PNJZM3QR"},"agent_actions":{"view_html":"https://pith.science/pith/PNJZM3QRPUV4A2ZG7Z7BPPKEQN","download_json":"https://pith.science/pith/PNJZM3QRPUV4A2ZG7Z7BPPKEQN.json","view_paper":"https://pith.science/paper/PNJZM3QR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.5376&json=true","fetch_graph":"https://pith.science/api/pith-number/PNJZM3QRPUV4A2ZG7Z7BPPKEQN/graph.json","fetch_events":"https://pith.science/api/pith-number/PNJZM3QRPUV4A2ZG7Z7BPPKEQN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PNJZM3QRPUV4A2ZG7Z7BPPKEQN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PNJZM3QRPUV4A2ZG7Z7BPPKEQN/action/storage_attestation","attest_author":"https://pith.science/pith/PNJZM3QRPUV4A2ZG7Z7BPPKEQN/action/author_attestation","sign_citation":"https://pith.science/pith/PNJZM3QRPUV4A2ZG7Z7BPPKEQN/action/citation_signature","submit_replication":"https://pith.science/pith/PNJZM3QRPUV4A2ZG7Z7BPPKEQN/action/replication_record"}},"created_at":"2026-05-18T01:22:25.454968+00:00","updated_at":"2026-05-18T01:22:25.454968+00:00"}