{"paper":{"title":"Simultaneously nonvanishing higher derived limits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CT"],"primary_cat":"math.LO","authors_text":"Chris Lambie-Hanson, Matteo Casarosa","submitted_at":"2024-11-24T14:20:56Z","abstract_excerpt":"The derived functors $\\lim^n$ of the inverse limit find many applications in algebra and topology. In particular, the vanishing of certain derived limits $\\lim^n \\mathbf{A}[H]$, parametrized by an abelian group $H$, has implications for strong homology and condensed mathematics. In this paper, we prove that if $\\mathfrak{d}=\\omega_n$, then $\\lim^n \\mathbf{A}[H] \\neq 0$ holds for $H=\\mathbb{Z}^{(\\omega_n)}$ (i.e. the direct sum of $\\omega_n$-many copies of $\\mathbb{Z}$). The same holds for $H=\\mathbb{Z}$ under the assumption that $\\mathrm{w}\\diamondsuit(S^{k+1}_k)$ holds for all $k < n$. In par"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15856","kind":"arxiv","version":2},"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/2411.15856/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"}