{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:P2MMMGIE6MCKW4MIFXVWOULXEL","short_pith_number":"pith:P2MMMGIE","schema_version":"1.0","canonical_sha256":"7e98c61904f304ab71882deb67517722edae95670da04ae1bc538e68eb6efe1d","source":{"kind":"arxiv","id":"1501.07759","version":2},"attestation_state":"computed","paper":{"title":"The Tate spectrum of the higher real $K$-theories at height $n=p-1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Drew Heard","submitted_at":"2015-01-30T12:53:02Z","abstract_excerpt":"Let $E_n$ be Morava $E$-theory and let $G \\subset G_n$ be a finite subgroup of $G_n$, the extended Morava stabilizer group. Let $E_{n}^{tG}$ be the Tate spectrum, defined as the cofiber of the norm map $N:(E_n)_{hG} \\to E_n^{hG}$. We use the Tate spectral sequence to calculate $\\pi_*E_{p-1}^{tG}$ for $G$ a maximal finite $p$-subgroup, and $p$ an odd prime. We show that $E_{p-1}^{tG} \\simeq \\ast$, so that the norm map gives equivalence between homotopy fixed point and homotopy orbit spectra. Our methods also give a calculation of $\\pi_*E_{p-1}^{hG}$, which is a folklore calculation of Hopkins a"},"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":"1501.07759","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-01-30T12:53:02Z","cross_cats_sorted":[],"title_canon_sha256":"a1ebec794859c9950ac8ffe17f257ad225b384523f315e497b3a66b276e824b8","abstract_canon_sha256":"20409b35dc0b2b7bfdf3bb3f77f6726d7ce744e1df9abc6182c8dcda024c0316"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:51.322608Z","signature_b64":"84fnRyZG0Z9HlspYZbxywnOcIkvu/ikStINo0vnbNGcozMI+FlkoaD87gozFQImHHkOXyMXTrYSXpvU5UZwYAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e98c61904f304ab71882deb67517722edae95670da04ae1bc538e68eb6efe1d","last_reissued_at":"2026-05-18T02:21:51.321932Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:51.321932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Tate spectrum of the higher real $K$-theories at height $n=p-1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Drew Heard","submitted_at":"2015-01-30T12:53:02Z","abstract_excerpt":"Let $E_n$ be Morava $E$-theory and let $G \\subset G_n$ be a finite subgroup of $G_n$, the extended Morava stabilizer group. Let $E_{n}^{tG}$ be the Tate spectrum, defined as the cofiber of the norm map $N:(E_n)_{hG} \\to E_n^{hG}$. We use the Tate spectral sequence to calculate $\\pi_*E_{p-1}^{tG}$ for $G$ a maximal finite $p$-subgroup, and $p$ an odd prime. We show that $E_{p-1}^{tG} \\simeq \\ast$, so that the norm map gives equivalence between homotopy fixed point and homotopy orbit spectra. Our methods also give a calculation of $\\pi_*E_{p-1}^{hG}$, which is a folklore calculation of Hopkins a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07759","kind":"arxiv","version":2},"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":"1501.07759","created_at":"2026-05-18T02:21:51.322029+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.07759v2","created_at":"2026-05-18T02:21:51.322029+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.07759","created_at":"2026-05-18T02:21:51.322029+00:00"},{"alias_kind":"pith_short_12","alias_value":"P2MMMGIE6MCK","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"P2MMMGIE6MCKW4MI","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"P2MMMGIE","created_at":"2026-05-18T12:29:34.919912+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/P2MMMGIE6MCKW4MIFXVWOULXEL","json":"https://pith.science/pith/P2MMMGIE6MCKW4MIFXVWOULXEL.json","graph_json":"https://pith.science/api/pith-number/P2MMMGIE6MCKW4MIFXVWOULXEL/graph.json","events_json":"https://pith.science/api/pith-number/P2MMMGIE6MCKW4MIFXVWOULXEL/events.json","paper":"https://pith.science/paper/P2MMMGIE"},"agent_actions":{"view_html":"https://pith.science/pith/P2MMMGIE6MCKW4MIFXVWOULXEL","download_json":"https://pith.science/pith/P2MMMGIE6MCKW4MIFXVWOULXEL.json","view_paper":"https://pith.science/paper/P2MMMGIE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.07759&json=true","fetch_graph":"https://pith.science/api/pith-number/P2MMMGIE6MCKW4MIFXVWOULXEL/graph.json","fetch_events":"https://pith.science/api/pith-number/P2MMMGIE6MCKW4MIFXVWOULXEL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P2MMMGIE6MCKW4MIFXVWOULXEL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P2MMMGIE6MCKW4MIFXVWOULXEL/action/storage_attestation","attest_author":"https://pith.science/pith/P2MMMGIE6MCKW4MIFXVWOULXEL/action/author_attestation","sign_citation":"https://pith.science/pith/P2MMMGIE6MCKW4MIFXVWOULXEL/action/citation_signature","submit_replication":"https://pith.science/pith/P2MMMGIE6MCKW4MIFXVWOULXEL/action/replication_record"}},"created_at":"2026-05-18T02:21:51.322029+00:00","updated_at":"2026-05-18T02:21:51.322029+00:00"}