{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:IZGCLCANXQDE5YHVRSRBCSFXLO","short_pith_number":"pith:IZGCLCAN","schema_version":"1.0","canonical_sha256":"464c25880dbc064ee0f58ca21148b75ba64cfeefa8ac1f17f5e720a317866fe0","source":{"kind":"arxiv","id":"1410.2322","version":1},"attestation_state":"computed","paper":{"title":"Third cohomology for Frobenius kernels and related structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Christopher P. Bendel, Cornelius Pillen, Daniel K. Nakano","submitted_at":"2014-10-09T00:46:43Z","abstract_excerpt":"Let $G$ be a simple simply connected group scheme defined over ${\\mathbb F}_{p}$ and $k$ be an algebraically closed field of characteristic $p>0$. Moreover, let $B$ be a Borel subgroup of $G$ and $U$ be the unipotent radical of $B$. In this paper the authors compute the third cohomology group for $B$ and its Frobenius kernels, $B_{r}$, with coefficients in a one-dimensional representation. These computations hold with relatively mild restrictions on the characteristic of the field. As a consequence of our calculations, the third ordinary Lie algebra cohomology group for ${\\mathfrak u}=\\text{Li"},"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":"1410.2322","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-10-09T00:46:43Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"03f1d83794100807fc5cd8afd5acaee2778f695491c44710a04bb5435fb6ddfe","abstract_canon_sha256":"d926248329733ee1435e357c347131186d6d93dabfb146543dfd13439e6dc115"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:46.684111Z","signature_b64":"brisfWYLayZ6ZWGGGpZfOPIY3+QaUF8EFHOsGGPtD9pk59VCirY8Ne0P7yNc2RddSbhZWph2v/YqVz3eWprZDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"464c25880dbc064ee0f58ca21148b75ba64cfeefa8ac1f17f5e720a317866fe0","last_reissued_at":"2026-05-18T02:40:46.683655Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:46.683655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Third cohomology for Frobenius kernels and related structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Christopher P. Bendel, Cornelius Pillen, Daniel K. Nakano","submitted_at":"2014-10-09T00:46:43Z","abstract_excerpt":"Let $G$ be a simple simply connected group scheme defined over ${\\mathbb F}_{p}$ and $k$ be an algebraically closed field of characteristic $p>0$. Moreover, let $B$ be a Borel subgroup of $G$ and $U$ be the unipotent radical of $B$. In this paper the authors compute the third cohomology group for $B$ and its Frobenius kernels, $B_{r}$, with coefficients in a one-dimensional representation. These computations hold with relatively mild restrictions on the characteristic of the field. As a consequence of our calculations, the third ordinary Lie algebra cohomology group for ${\\mathfrak u}=\\text{Li"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2322","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":"1410.2322","created_at":"2026-05-18T02:40:46.683719+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.2322v1","created_at":"2026-05-18T02:40:46.683719+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2322","created_at":"2026-05-18T02:40:46.683719+00:00"},{"alias_kind":"pith_short_12","alias_value":"IZGCLCANXQDE","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"IZGCLCANXQDE5YHV","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"IZGCLCAN","created_at":"2026-05-18T12:28:33.132498+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/IZGCLCANXQDE5YHVRSRBCSFXLO","json":"https://pith.science/pith/IZGCLCANXQDE5YHVRSRBCSFXLO.json","graph_json":"https://pith.science/api/pith-number/IZGCLCANXQDE5YHVRSRBCSFXLO/graph.json","events_json":"https://pith.science/api/pith-number/IZGCLCANXQDE5YHVRSRBCSFXLO/events.json","paper":"https://pith.science/paper/IZGCLCAN"},"agent_actions":{"view_html":"https://pith.science/pith/IZGCLCANXQDE5YHVRSRBCSFXLO","download_json":"https://pith.science/pith/IZGCLCANXQDE5YHVRSRBCSFXLO.json","view_paper":"https://pith.science/paper/IZGCLCAN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.2322&json=true","fetch_graph":"https://pith.science/api/pith-number/IZGCLCANXQDE5YHVRSRBCSFXLO/graph.json","fetch_events":"https://pith.science/api/pith-number/IZGCLCANXQDE5YHVRSRBCSFXLO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IZGCLCANXQDE5YHVRSRBCSFXLO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IZGCLCANXQDE5YHVRSRBCSFXLO/action/storage_attestation","attest_author":"https://pith.science/pith/IZGCLCANXQDE5YHVRSRBCSFXLO/action/author_attestation","sign_citation":"https://pith.science/pith/IZGCLCANXQDE5YHVRSRBCSFXLO/action/citation_signature","submit_replication":"https://pith.science/pith/IZGCLCANXQDE5YHVRSRBCSFXLO/action/replication_record"}},"created_at":"2026-05-18T02:40:46.683719+00:00","updated_at":"2026-05-18T02:40:46.683719+00:00"}