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When $G$ is a $p$-group, we show that the layers in the filtration are the Steinberg summands of the equivariant classifying spaces of $(\\mathbb{Z}/p)^n$ for $n=0, 1, 2, \\ldots$. We show that the layers of the filtration split after smashing with $H\\underline{\\mathbb{F}}_p$. Along the way, we produced a general computation of the geometric fixed points of $H\\underline{\\mathbb{Z}}$ and"},"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":"1904.01708","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-04-02T23:28:12Z","cross_cats_sorted":[],"title_canon_sha256":"611f66d6018ea56739e846445e5c01db3c3c4ce576ba43e73680a5cd19fa7078","abstract_canon_sha256":"00903f5b721ee3aa17bd58236bef86437d369d3a9a4cbfcf3de353ac76edc869"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:30.079040Z","signature_b64":"Idu0agSvE1wt73HVp5BM0u8NvkaDHzUYcQ1Fpm5d2Ru7NFnPYKrREt45/qSf/okIHQPuE6U9AMgPUDPzBnCCCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e6d80497921c1cbf41f69322b115d3d4bf26032ef2dd8862d87e5dbbab0771e","last_reissued_at":"2026-05-17T23:49:30.078470Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:30.078470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symmetric Powers and Eilenberg--Maclane Spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Krishanu Sankar","submitted_at":"2019-04-02T23:28:12Z","abstract_excerpt":"We filter the equivariant Eilenberg Maclane spectrum $H\\underline{\\mathbb{F}}_p$ using the mod $p$ symmetric powers of the equivariant sphere spectrum, $\\mathrm{Sp}_{\\mathbb{Z}/p}^{\\infty}(\\Sigma^{\\infty G}S^0)$. 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