{"paper":{"title":"Permutation twisted cohomology, remixed","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.AG","math.CT","math.GR"],"primary_cat":"math.RT","authors_text":"Sam K. Miller","submitted_at":"2025-08-31T18:15:29Z","abstract_excerpt":"For each endotrivial complex for a $p$-group arising from Bredon homology of a representation sphere, we construct $p$-local quasi-isomorphisms, called forerunners. These enable us to extend Balmer--Gallauer's results in arXiv:2307.04398 concerning the tensor-triangular geometry of permutation modules for elementary abelian $p$-groups to all $p$-groups. We construct an open cover of the Balmer spectrum under which all endotrivials are tt-line bundles, that is, every endotrivial is locally isomorphic to a shift of the tensor unit. We define a remixed permutation twisted cohomology ring for whic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.00954","kind":"arxiv","version":4},"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/2509.00954/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"}