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This result generalizes the computation of arXiv:2303.12271 for finite $p$-groups, where $p$ is an odd prime. Finally, by comparing the Bousfield classes of $KU_G/p$ and $G$-equivariant Morava $K$-theory, we prove that the $KU_G/p$-local sphere spectrum is equivalent to a wedge sum of equivaria"},"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":"2605.30285","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2026-05-28T17:38:49Z","cross_cats_sorted":[],"title_canon_sha256":"34e018da82f08c1d46b110284234dcc1f8beffba6ecbaacd9bb4630938947382","abstract_canon_sha256":"e77e4cd617da458351bb2535d77750abd2a99f9931e2338eb320183fd00ce5a8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T02:06:15.249212Z","signature_b64":"w4faWMINuTtAxzRt8ukdNsw2RJoAn5Hp+hOCjjHW//MXVhfdN4l1WFpn1GjcCrliR7ukg9r+lzb9k4k6Dcb2Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20831e3e60c6eb6ec0d18b7540698163c0a6ec3ba8bf150054db8ce4d4b0e324","last_reissued_at":"2026-05-29T02:06:15.248744Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T02:06:15.248744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the equivariant $KU_G$ local sphere for finite abelian groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Yingxin Li","submitted_at":"2026-05-28T17:38:49Z","abstract_excerpt":"Given a finite abelian group $G$ and a Sylow $p$-subgroup $N_p$, we prove that the $KU_G/p$-local sphere spectrum is equivalent to the homotopy fixed points of a $p$-complete $KO_{N_p}$-module spectrum. 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