{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:MX4VQBZP5RN4YEZNVNV55Y2TOW","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":"9616e0f327d4ffb90d93f5781642f2627dde05dab0e274b7c8ba195d92976c08","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-05-15T15:00:37Z","title_canon_sha256":"b5388269e15a00be809dba815caf445b0ac91e9262ea1ff4e250bcb41df3066b"},"schema_version":"1.0","source":{"id":"2305.08699","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.08699","created_at":"2026-07-05T07:40:21Z"},{"alias_kind":"arxiv_version","alias_value":"2305.08699v4","created_at":"2026-07-05T07:40:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.08699","created_at":"2026-07-05T07:40:21Z"},{"alias_kind":"pith_short_12","alias_value":"MX4VQBZP5RN4","created_at":"2026-07-05T07:40:21Z"},{"alias_kind":"pith_short_16","alias_value":"MX4VQBZP5RN4YEZN","created_at":"2026-07-05T07:40:21Z"},{"alias_kind":"pith_short_8","alias_value":"MX4VQBZP","created_at":"2026-07-05T07:40:21Z"}],"graph_snapshots":[{"event_id":"sha256:5e81ba28f2b4b1bd74256160ff2c8784b21792a6ac1009b5d2d56364edaeb805","target":"graph","created_at":"2026-07-05T07:40:21Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2305.08699/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"If k is an arbitrary field, we construct a category of k-1-motives in which every commutative algebraic k-group G has a dual object $G^{\\vee}$. When k is a local field of arbitrary characteristic, we establish Pontryagin duality theorems that relate the fppf cohomology groups of G to the hypercohomology groups of the k-1-motive $G^{\\vee}$. We also obtain a duality theorem for the second cohomology group of an arbitrary k-1-motive. These results have applications (to be discussed elsewhere) to certain extensions of Lichtenbaum-van Hamel duality to a class of non-smooth proper k-varieties.","authors_text":"Cristian D. Gonzalez-Aviles","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-05-15T15:00:37Z","title":"Local duality theorems for commutative algebraic groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.08699","kind":"arxiv","version":4},"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:eb11ce4ea6588243268943c16996891c08b6a34ba4fb50ea531e6b3ae1a32b18","target":"record","created_at":"2026-07-05T07:40:21Z","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":"9616e0f327d4ffb90d93f5781642f2627dde05dab0e274b7c8ba195d92976c08","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-05-15T15:00:37Z","title_canon_sha256":"b5388269e15a00be809dba815caf445b0ac91e9262ea1ff4e250bcb41df3066b"},"schema_version":"1.0","source":{"id":"2305.08699","kind":"arxiv","version":4}},"canonical_sha256":"65f958072fec5bcc132dab6bdee35375abe4f0b7db20a9769356dbff5fb7600b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65f958072fec5bcc132dab6bdee35375abe4f0b7db20a9769356dbff5fb7600b","first_computed_at":"2026-07-05T07:40:21.454990Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:40:21.454990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"piyBxWSsRXhiloGSVdPAKCt5IRQKojlYX6+SURAH9VeXNCmO2aWI2LzuAA9z2gQLVhUTwI4yrQqiCddCuq/mBw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:40:21.455449Z","signed_message":"canonical_sha256_bytes"},"source_id":"2305.08699","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb11ce4ea6588243268943c16996891c08b6a34ba4fb50ea531e6b3ae1a32b18","sha256:5e81ba28f2b4b1bd74256160ff2c8784b21792a6ac1009b5d2d56364edaeb805"],"state_sha256":"eab6341989c0b90b8ca72fb5e74305648c710643a31de18d2de5e1e746bcc5d7"}