{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:KC7ULGJYDQJZGWKRPG4FJLNKS5","short_pith_number":"pith:KC7ULGJY","schema_version":"1.0","canonical_sha256":"50bf4599381c1393595179b854adaa977101cd0f38f6471a0c0edb438ad72414","source":{"kind":"arxiv","id":"0804.4246","version":5},"attestation_state":"computed","paper":{"title":"Finite generation of Tate cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.RT","authors_text":"Jan Minac, Jon F. Carlson, Sunil K. Chebolu","submitted_at":"2008-04-26T19:16:23Z","abstract_excerpt":"Let G be a finite group and let k be a field of characteristic p. Given a finitely generated indecomposable non-projective kG-module M, we conjecture that if the Tate cohomology $\\HHHH^*(G, M)$ of G with coefficients in M is finitely generated over the Tate cohomology ring $\\HHHH^*(G, k)$, then the support variety V_G(M) of M is equal to the entire maximal ideal spectrum V_G(k). We prove various results which support this conjecture. The converse of this conjecture is established for modules in the connected component of k in the stable Auslander-Reiten quiver for kG, but it is shown to be fal"},"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":"0804.4246","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2008-04-26T19:16:23Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"18ab0874366b4ea3a63f77cdc11cac1c3d6e21ebee1f2082fc58e3707a0a5b6f","abstract_canon_sha256":"fa8a9163c5598d947b40676bf1ba06c25d8de99644e2be8d95b9e1ddea538cd5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:35.395908Z","signature_b64":"fBGWBQWkKAdREp0VaAozH5avFikYs2XzJr6WDCeG4eRZRcdIc3MdWkufp8Qp4Zb61L06XEaZ/FJGv+kWtlu2Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50bf4599381c1393595179b854adaa977101cd0f38f6471a0c0edb438ad72414","last_reissued_at":"2026-05-18T04:09:35.395436Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:35.395436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite generation of Tate cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.RT","authors_text":"Jan Minac, Jon F. Carlson, Sunil K. Chebolu","submitted_at":"2008-04-26T19:16:23Z","abstract_excerpt":"Let G be a finite group and let k be a field of characteristic p. Given a finitely generated indecomposable non-projective kG-module M, we conjecture that if the Tate cohomology $\\HHHH^*(G, M)$ of G with coefficients in M is finitely generated over the Tate cohomology ring $\\HHHH^*(G, k)$, then the support variety V_G(M) of M is equal to the entire maximal ideal spectrum V_G(k). We prove various results which support this conjecture. The converse of this conjecture is established for modules in the connected component of k in the stable Auslander-Reiten quiver for kG, but it is shown to be fal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.4246","kind":"arxiv","version":5},"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":"0804.4246","created_at":"2026-05-18T04:09:35.395515+00:00"},{"alias_kind":"arxiv_version","alias_value":"0804.4246v5","created_at":"2026-05-18T04:09:35.395515+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0804.4246","created_at":"2026-05-18T04:09:35.395515+00:00"},{"alias_kind":"pith_short_12","alias_value":"KC7ULGJYDQJZ","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"KC7ULGJYDQJZGWKR","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"KC7ULGJY","created_at":"2026-05-18T12:25:57.157939+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/KC7ULGJYDQJZGWKRPG4FJLNKS5","json":"https://pith.science/pith/KC7ULGJYDQJZGWKRPG4FJLNKS5.json","graph_json":"https://pith.science/api/pith-number/KC7ULGJYDQJZGWKRPG4FJLNKS5/graph.json","events_json":"https://pith.science/api/pith-number/KC7ULGJYDQJZGWKRPG4FJLNKS5/events.json","paper":"https://pith.science/paper/KC7ULGJY"},"agent_actions":{"view_html":"https://pith.science/pith/KC7ULGJYDQJZGWKRPG4FJLNKS5","download_json":"https://pith.science/pith/KC7ULGJYDQJZGWKRPG4FJLNKS5.json","view_paper":"https://pith.science/paper/KC7ULGJY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0804.4246&json=true","fetch_graph":"https://pith.science/api/pith-number/KC7ULGJYDQJZGWKRPG4FJLNKS5/graph.json","fetch_events":"https://pith.science/api/pith-number/KC7ULGJYDQJZGWKRPG4FJLNKS5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KC7ULGJYDQJZGWKRPG4FJLNKS5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KC7ULGJYDQJZGWKRPG4FJLNKS5/action/storage_attestation","attest_author":"https://pith.science/pith/KC7ULGJYDQJZGWKRPG4FJLNKS5/action/author_attestation","sign_citation":"https://pith.science/pith/KC7ULGJYDQJZGWKRPG4FJLNKS5/action/citation_signature","submit_replication":"https://pith.science/pith/KC7ULGJYDQJZGWKRPG4FJLNKS5/action/replication_record"}},"created_at":"2026-05-18T04:09:35.395515+00:00","updated_at":"2026-05-18T04:09:35.395515+00:00"}