{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:UHI57S2JGK3QEYGE3PKQFO2JGO","short_pith_number":"pith:UHI57S2J","schema_version":"1.0","canonical_sha256":"a1d1dfcb4932b70260c4dbd502bb49338932314acdf0149666e456933b16813c","source":{"kind":"arxiv","id":"1908.01898","version":1},"attestation_state":"computed","paper":{"title":"A lift from group cohomology to spectra for trivial profinite actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Daniel G. Davis","submitted_at":"2019-08-05T23:09:20Z","abstract_excerpt":"Let $G$ be a profinite group, $X$ a discrete $G$-spectrum with trivial action, and $X^{hG}$ the continuous homotopy fixed points. For any $N \\trianglelefteq_o G$ (\"$o$\" for open), $X = X^N$ is a $G/N$-spectrum with trivial action. We construct a zigzag $\\text{colim}\\,_N \\,X^{hG/N} \\buildrel\\Phi\\over\\longrightarrow \\text{colim}\\,_N \\,(X^{hN})^{hG/N} \\buildrel\\Psi\\over\\longleftarrow X^{hG}$, where $\\Psi$ is a weak equivalence. When $\\Phi$ is a weak equivalence, this zigzag gives an interesting model for $X^{hG}$ (for example, its Spanier-Whitehead dual is $\\text{holim}\\,_N \\,F(X^{hG/N}, S^0)$). "},"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":"1908.01898","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-08-05T23:09:20Z","cross_cats_sorted":[],"title_canon_sha256":"19bc17d106341f641c0014dbe1666d33a675d58412bdda4283c7cb096c81c510","abstract_canon_sha256":"f089910a905dff7cad880d6fe79bead6f29f0d978502d6cf5b3e14f4a08b524d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:51:48.818566Z","signature_b64":"l7GMT4HRij7nCDA9H6nr/7lSUveRM0ymxn5VHNBJLmfeo2h91FbL0ptDjSsIeP3jPv1S+dn6ThxiVgg8tbKMAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a1d1dfcb4932b70260c4dbd502bb49338932314acdf0149666e456933b16813c","last_reissued_at":"2026-07-04T23:51:48.818155Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:51:48.818155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A lift from group cohomology to spectra for trivial profinite actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Daniel G. Davis","submitted_at":"2019-08-05T23:09:20Z","abstract_excerpt":"Let $G$ be a profinite group, $X$ a discrete $G$-spectrum with trivial action, and $X^{hG}$ the continuous homotopy fixed points. For any $N \\trianglelefteq_o G$ (\"$o$\" for open), $X = X^N$ is a $G/N$-spectrum with trivial action. We construct a zigzag $\\text{colim}\\,_N \\,X^{hG/N} \\buildrel\\Phi\\over\\longrightarrow \\text{colim}\\,_N \\,(X^{hN})^{hG/N} \\buildrel\\Psi\\over\\longleftarrow X^{hG}$, where $\\Psi$ is a weak equivalence. When $\\Phi$ is a weak equivalence, this zigzag gives an interesting model for $X^{hG}$ (for example, its Spanier-Whitehead dual is $\\text{holim}\\,_N \\,F(X^{hG/N}, S^0)$). "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01898","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.01898/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1908.01898","created_at":"2026-07-04T23:51:48.818217+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.01898v1","created_at":"2026-07-04T23:51:48.818217+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.01898","created_at":"2026-07-04T23:51:48.818217+00:00"},{"alias_kind":"pith_short_12","alias_value":"UHI57S2JGK3Q","created_at":"2026-07-04T23:51:48.818217+00:00"},{"alias_kind":"pith_short_16","alias_value":"UHI57S2JGK3QEYGE","created_at":"2026-07-04T23:51:48.818217+00:00"},{"alias_kind":"pith_short_8","alias_value":"UHI57S2J","created_at":"2026-07-04T23:51:48.818217+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/UHI57S2JGK3QEYGE3PKQFO2JGO","json":"https://pith.science/pith/UHI57S2JGK3QEYGE3PKQFO2JGO.json","graph_json":"https://pith.science/api/pith-number/UHI57S2JGK3QEYGE3PKQFO2JGO/graph.json","events_json":"https://pith.science/api/pith-number/UHI57S2JGK3QEYGE3PKQFO2JGO/events.json","paper":"https://pith.science/paper/UHI57S2J"},"agent_actions":{"view_html":"https://pith.science/pith/UHI57S2JGK3QEYGE3PKQFO2JGO","download_json":"https://pith.science/pith/UHI57S2JGK3QEYGE3PKQFO2JGO.json","view_paper":"https://pith.science/paper/UHI57S2J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.01898&json=true","fetch_graph":"https://pith.science/api/pith-number/UHI57S2JGK3QEYGE3PKQFO2JGO/graph.json","fetch_events":"https://pith.science/api/pith-number/UHI57S2JGK3QEYGE3PKQFO2JGO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UHI57S2JGK3QEYGE3PKQFO2JGO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UHI57S2JGK3QEYGE3PKQFO2JGO/action/storage_attestation","attest_author":"https://pith.science/pith/UHI57S2JGK3QEYGE3PKQFO2JGO/action/author_attestation","sign_citation":"https://pith.science/pith/UHI57S2JGK3QEYGE3PKQFO2JGO/action/citation_signature","submit_replication":"https://pith.science/pith/UHI57S2JGK3QEYGE3PKQFO2JGO/action/replication_record"}},"created_at":"2026-07-04T23:51:48.818217+00:00","updated_at":"2026-07-04T23:51:48.818217+00:00"}