{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NNQBPCHVAUM3ZUYYIKBA4LKESZ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6972291bf3eec17a4f9bdb1cffe9b76872bafc56a48f1eaf674f8bb46c06dc4b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-02T11:36:01Z","title_canon_sha256":"66e3d464c537bb7de86a1abe67d8014e19f438453308505977d4fd5e05068c38"},"schema_version":"1.0","source":{"id":"1308.0472","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0472","created_at":"2026-05-18T03:16:50Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0472v1","created_at":"2026-05-18T03:16:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0472","created_at":"2026-05-18T03:16:50Z"},{"alias_kind":"pith_short_12","alias_value":"NNQBPCHVAUM3","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NNQBPCHVAUM3ZUYY","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NNQBPCHV","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:d77a26c99a4be8d6320f54a6945dd01c3018c6dca11fba510ba6624b3e2880c9","target":"graph","created_at":"2026-05-18T03:16:50Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We define 1-motives of a variety X over a perfect field of positive characteristic which realize the etale cohomology groups of X in dimension and codimension one. This is the analogue in positive characteristic of previous results of Barbieri-Viale and Srinivas, except that we only consider the etale realization but also consider compactly supported cohomology. The dimension-1 case (called the Picard 1-motives) can be done by standard techniques, and indeed this case is probably well known. But the codimension-one case (Albanese 1-motive) requires stronger tools, namely a strong version of de","authors_text":"Peter Mannisto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-02T11:36:01Z","title":"Albanese and Picard 1-Motives in Positive Characteristic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0472","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3467f95f963f430d4b59ec29f5a244c2e8f4807e34929bf1275c1eb24523b0a2","target":"record","created_at":"2026-05-18T03:16:50Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6972291bf3eec17a4f9bdb1cffe9b76872bafc56a48f1eaf674f8bb46c06dc4b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-02T11:36:01Z","title_canon_sha256":"66e3d464c537bb7de86a1abe67d8014e19f438453308505977d4fd5e05068c38"},"schema_version":"1.0","source":{"id":"1308.0472","kind":"arxiv","version":1}},"canonical_sha256":"6b601788f50519bcd31842820e2d4496733ebeccc25206f277f7835d2b6d6bdf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b601788f50519bcd31842820e2d4496733ebeccc25206f277f7835d2b6d6bdf","first_computed_at":"2026-05-18T03:16:50.386361Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:50.386361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ijH7uvAXzSSlkHzfMOsntddzgYY5I18F2cgzP72aBH2miDgykpEwfZ0eO0b80cihr94/zkd9eJAzA83PWJhhCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:50.387164Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.0472","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3467f95f963f430d4b59ec29f5a244c2e8f4807e34929bf1275c1eb24523b0a2","sha256:d77a26c99a4be8d6320f54a6945dd01c3018c6dca11fba510ba6624b3e2880c9"],"state_sha256":"84966bf9abc2f7f9833e23b976afc6e50cf399fe977b24e10defa73a90cf9784"}