{"paper":{"title":"Global representation theory: Homological foundations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CT"],"primary_cat":"math.RT","authors_text":"Jordan Williamson, Luca Pol, Miguel Barrero, Neil Strickland, Tobias Barthel","submitted_at":"2025-05-27T17:21:22Z","abstract_excerpt":"A global representation is a compatible collection of representations of the outer automorphism groups of the groups belonging to some collection of finite groups $\\mathscr{U}$. Global representations assemble into an abelian category $\\mathsf{A}(\\mathscr{U})$, simultaneously generalising classical representation theory and the category of VI-modules appearing in the representation theory of the general linear groups. In this paper we establish homological foundations of its derived category $\\mathsf{D}(\\mathscr{U})$. We prove that any complex of projective global representations is DG-project"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21449","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/2505.21449/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"}