{"paper":{"title":"The homological slice spectral sequence in motivic and Real bordism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Christian Carrick, Douglas C. Ravenel, Michael A. Hill","submitted_at":"2023-04-04T17:09:40Z","abstract_excerpt":"For a motivic spectrum $E\\in \\mathcal{SH}(k)$, let $\\Gamma(E)$ denote the global sections spectrum, where $E$ is viewed as a sheaf of spectra on $\\mathrm{Sm}_k$. Voevodsky's slice filtration determines a spectral sequence converging to the homotopy groups of $\\Gamma(E)$. In this paper, we introduce a spectral sequence converging instead to the mod 2 homology of $\\Gamma(E)$ and study the case $E=BPGL\\langle m\\rangle$ for $k=\\mathbb R$ in detail. We show that this spectral sequence contains the $\\mathcal{A}_*$-comodule algebra $(\\mathcal{A}//\\mathcal{A}(m))^*$ as permanent cycles, and we determi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.01960","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2304.01960/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}