{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:7UCCJCMJZWWUL2QKP3HRCYAEOH","short_pith_number":"pith:7UCCJCMJ","schema_version":"1.0","canonical_sha256":"fd04248989cdad45ea0a7ecf11600471e306b41fa8f92a8a5c957263febe25c2","source":{"kind":"arxiv","id":"1703.10850","version":1},"attestation_state":"computed","paper":{"title":"Constructibilit\\'e et mod\\'eration uniformes en cohomologie \\'etale","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Fabrice Orgogozo","submitted_at":"2017-03-31T11:08:15Z","abstract_excerpt":"Let S be a Noetherian scheme and f:X -> S a proper morphism. By SGA 4 XIV, for any constructible sheaf F of Z/nZ-modules on X, the sheaves of Z/nZ-modules R^if_*F obtained by direct image (for the etale topology) are also constructible: there is a stratification of S on whose strata these sheaves are locally constant constructible. After previous work of N. Katz and G. Laumon, or L. Illusie, on the special case in which S is generically of characteristic zero or the sheaves F are constant (with invertible torsion on S), here we study the dependency of the stratification on F. We show that a na"},"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":"1703.10850","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-03-31T11:08:15Z","cross_cats_sorted":[],"title_canon_sha256":"7e36cbd248900932df2549a930d99356be891744cab1f24499d70ee8779fade2","abstract_canon_sha256":"87941e78211e19e90d6f312bba0a631ee863ce732b9b1c9d1cfbff2771302c80"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:16.494658Z","signature_b64":"zpa/9N4TEpb8t/O2D5pVaxSIHrJ2xgS70s+LqOu58rMZVhJO14rs97LKPTYhBn0w+QmmIRA90gpJlrngGj2KBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd04248989cdad45ea0a7ecf11600471e306b41fa8f92a8a5c957263febe25c2","last_reissued_at":"2026-05-17T23:50:16.494007Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:16.494007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Constructibilit\\'e et mod\\'eration uniformes en cohomologie \\'etale","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Fabrice Orgogozo","submitted_at":"2017-03-31T11:08:15Z","abstract_excerpt":"Let S be a Noetherian scheme and f:X -> S a proper morphism. By SGA 4 XIV, for any constructible sheaf F of Z/nZ-modules on X, the sheaves of Z/nZ-modules R^if_*F obtained by direct image (for the etale topology) are also constructible: there is a stratification of S on whose strata these sheaves are locally constant constructible. After previous work of N. Katz and G. Laumon, or L. Illusie, on the special case in which S is generically of characteristic zero or the sheaves F are constant (with invertible torsion on S), here we study the dependency of the stratification on F. We show that a na"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10850","kind":"arxiv","version":1},"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":"1703.10850","created_at":"2026-05-17T23:50:16.494078+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.10850v1","created_at":"2026-05-17T23:50:16.494078+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.10850","created_at":"2026-05-17T23:50:16.494078+00:00"},{"alias_kind":"pith_short_12","alias_value":"7UCCJCMJZWWU","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_16","alias_value":"7UCCJCMJZWWUL2QK","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_8","alias_value":"7UCCJCMJ","created_at":"2026-05-18T12:31:05.417338+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/7UCCJCMJZWWUL2QKP3HRCYAEOH","json":"https://pith.science/pith/7UCCJCMJZWWUL2QKP3HRCYAEOH.json","graph_json":"https://pith.science/api/pith-number/7UCCJCMJZWWUL2QKP3HRCYAEOH/graph.json","events_json":"https://pith.science/api/pith-number/7UCCJCMJZWWUL2QKP3HRCYAEOH/events.json","paper":"https://pith.science/paper/7UCCJCMJ"},"agent_actions":{"view_html":"https://pith.science/pith/7UCCJCMJZWWUL2QKP3HRCYAEOH","download_json":"https://pith.science/pith/7UCCJCMJZWWUL2QKP3HRCYAEOH.json","view_paper":"https://pith.science/paper/7UCCJCMJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.10850&json=true","fetch_graph":"https://pith.science/api/pith-number/7UCCJCMJZWWUL2QKP3HRCYAEOH/graph.json","fetch_events":"https://pith.science/api/pith-number/7UCCJCMJZWWUL2QKP3HRCYAEOH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7UCCJCMJZWWUL2QKP3HRCYAEOH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7UCCJCMJZWWUL2QKP3HRCYAEOH/action/storage_attestation","attest_author":"https://pith.science/pith/7UCCJCMJZWWUL2QKP3HRCYAEOH/action/author_attestation","sign_citation":"https://pith.science/pith/7UCCJCMJZWWUL2QKP3HRCYAEOH/action/citation_signature","submit_replication":"https://pith.science/pith/7UCCJCMJZWWUL2QKP3HRCYAEOH/action/replication_record"}},"created_at":"2026-05-17T23:50:16.494078+00:00","updated_at":"2026-05-17T23:50:16.494078+00:00"}