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When $R$ is an Eilenberg-Mac Lane spectrum, in some good cases such an extension is a $G$-Galois extension in the sense of John Rognes, but not always faithful. We prove that for $E_n$ and $K_n$ these extensions are always faithful in the $K_n$ local category. However, for a cyclic $p$-group $C_{p^r}$, the cochain extension $F({BC_{p^r}}_+,E_n) \\to F({EC_{p^r}}_+,E_n)$ is not a Galois extensions because it"},"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":"1005.1662","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-05-10T20:18:14Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"e3b1421b0c056953b515661f5b0ced489f825483c93cce1ee70942106f962572","abstract_canon_sha256":"60a7c179c446044fa4a76716f70726642dbb3b651a49a5d7aa08d3910f3595a4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:00.700298Z","signature_b64":"asWc3XgghtzYqJrwYj+1aRnN6gzWQXgQbyYfAojudF6Qb6s9IpzOgnZwDfGt+oOc60ELggEvMR+ZE7xvVjTgBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1bbf47b8593b3e09a0320548ad8f7aa59b991d751166b2619b70676eaf631663","last_reissued_at":"2026-05-18T04:21:00.699756Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:00.699756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some properties of Lubin-Tate cohomology for classifying spaces of finite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AT","authors_text":"Andrew Baker, Birgit Richter","submitted_at":"2010-05-10T20:18:14Z","abstract_excerpt":"We consider brave new cochain extensions $F(BG_+,R)\\to F(EG_+,R)$, where $R$ is either a Lubin-Tate spectrum $E_n$ or the related 2-periodic Morava K-theory $K_n$, and $G$ is a finite group. 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