{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:5BPRY2RTRZVLSTFADCIXB33WEM","short_pith_number":"pith:5BPRY2RT","schema_version":"1.0","canonical_sha256":"e85f1c6a338e6ab94ca0189170ef7623374053eed1bb8d146b5d811be9f6df96","source":{"kind":"arxiv","id":"1309.1198","version":2},"attestation_state":"computed","paper":{"title":"The pro-\\'etale topology for schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Bhargav Bhatt, Peter Scholze","submitted_at":"2013-09-04T22:22:25Z","abstract_excerpt":"We give a new definition of the derived category of constructible $\\ell$-adic sheaves on a scheme, which is as simple as the geometric intuition behind them. Moreover, we define a refined fundamental group of schemes, which is large enough to see all lisse $\\ell$-adic sheaves, even on non-normal schemes. To accomplish these tasks, we define and study the pro-\\'etale topology, which is a Grothendieck topology on schemes that is closely related to the \\'etale topology, and yet better suited for infinite constructions typically encountered in $\\ell$-adic cohomology. An essential foundational resu"},"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":"1309.1198","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-09-04T22:22:25Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"e86505ae031cf7b7f38466d986eb759a1479ab81912fcd74381e5dd73f0e7cb5","abstract_canon_sha256":"6ece64ffd388484cdad298229bd325ae16d20fa7adca6992b0ac6706967dda2b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:04.072707Z","signature_b64":"knniuLy0RXEKvKygv963qXolfKePpGylkSisIImNSlpSvnF85bBN8KlqnHmx3ryns9ofgM4UPbjz/HuHHndjAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e85f1c6a338e6ab94ca0189170ef7623374053eed1bb8d146b5d811be9f6df96","last_reissued_at":"2026-05-18T02:31:04.072237Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:04.072237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The pro-\\'etale topology for schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Bhargav Bhatt, Peter Scholze","submitted_at":"2013-09-04T22:22:25Z","abstract_excerpt":"We give a new definition of the derived category of constructible $\\ell$-adic sheaves on a scheme, which is as simple as the geometric intuition behind them. Moreover, we define a refined fundamental group of schemes, which is large enough to see all lisse $\\ell$-adic sheaves, even on non-normal schemes. To accomplish these tasks, we define and study the pro-\\'etale topology, which is a Grothendieck topology on schemes that is closely related to the \\'etale topology, and yet better suited for infinite constructions typically encountered in $\\ell$-adic cohomology. An essential foundational resu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1198","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":"1309.1198","created_at":"2026-05-18T02:31:04.072302+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.1198v2","created_at":"2026-05-18T02:31:04.072302+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1198","created_at":"2026-05-18T02:31:04.072302+00:00"},{"alias_kind":"pith_short_12","alias_value":"5BPRY2RTRZVL","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_16","alias_value":"5BPRY2RTRZVLSTFA","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_8","alias_value":"5BPRY2RT","created_at":"2026-05-18T12:27:34.582898+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2603.15048","citing_title":"Homomorphisms of topological rings and change-of-scalar functors","ref_index":5,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5BPRY2RTRZVLSTFADCIXB33WEM","json":"https://pith.science/pith/5BPRY2RTRZVLSTFADCIXB33WEM.json","graph_json":"https://pith.science/api/pith-number/5BPRY2RTRZVLSTFADCIXB33WEM/graph.json","events_json":"https://pith.science/api/pith-number/5BPRY2RTRZVLSTFADCIXB33WEM/events.json","paper":"https://pith.science/paper/5BPRY2RT"},"agent_actions":{"view_html":"https://pith.science/pith/5BPRY2RTRZVLSTFADCIXB33WEM","download_json":"https://pith.science/pith/5BPRY2RTRZVLSTFADCIXB33WEM.json","view_paper":"https://pith.science/paper/5BPRY2RT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.1198&json=true","fetch_graph":"https://pith.science/api/pith-number/5BPRY2RTRZVLSTFADCIXB33WEM/graph.json","fetch_events":"https://pith.science/api/pith-number/5BPRY2RTRZVLSTFADCIXB33WEM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5BPRY2RTRZVLSTFADCIXB33WEM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5BPRY2RTRZVLSTFADCIXB33WEM/action/storage_attestation","attest_author":"https://pith.science/pith/5BPRY2RTRZVLSTFADCIXB33WEM/action/author_attestation","sign_citation":"https://pith.science/pith/5BPRY2RTRZVLSTFADCIXB33WEM/action/citation_signature","submit_replication":"https://pith.science/pith/5BPRY2RTRZVLSTFADCIXB33WEM/action/replication_record"}},"created_at":"2026-05-18T02:31:04.072302+00:00","updated_at":"2026-05-18T02:31:04.072302+00:00"}