{"paper":{"title":"The Euler characteristic of an endotrivial complex","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GR","math.KT"],"primary_cat":"math.RT","authors_text":"Nadia Mazza, Sam K. Miller","submitted_at":"2025-08-10T16:05:18Z","abstract_excerpt":"Let $G$ be a finite group and $k$ a field of prime characteristic $p$. We examine the Lefschetz homomorphism $\\Lambda: \\mathcal{E}_k(G) \\to O(T(kG))$ from the group of endotrivial complexes, i.e. the Picard group of the bounded homotopy category of $p$-permutation modules $K^b({}_{kG}\\mathbf{triv})$, to the orthogonal unit group of the Grothendieck group of $K^b({}_{kG}\\mathbf{triv})$, i.e. the trivial source ring. When $p = 2$ and $k = \\mathbb{F}_2$, $\\Lambda$ is surjective when $G$ has a Sylow $2$-subgroup with fusion controlled by its normalizer, and when $G$ has dihedral Sylow $2$-subgroup"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.07404","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/2508.07404/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"}