{"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, $\\mathrm{Sp}_{\\mathbb{Z}/p}^{\\infty}(\\Sigma^{\\infty G}S^0)$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.01708","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":""},"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"}