{"paper":{"title":"Representation Stability for Families of Linear Subspace Arrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.AT","math.RT"],"primary_cat":"math.GT","authors_text":"Nir Gadish","submitted_at":"2016-03-28T20:23:27Z","abstract_excerpt":"Church-Ellenberg-Farb used the language of FI-modules to prove that the cohomology of certain sequences of hyperplane arrangements with S_n-actions satisfies representation stability. Here we lift their results to the level of the arrangements themselves, and define when a collection of arrangements is \"finitely generated\". Using this notion we greatly widen the stability results to:\n  1) General linear subspace arrangements, not necessarily of hyperplanes.\n  2) A wide class of group actions, replacing FI by a general category C.\n  We show that the cohomology of such collections of arrangement"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08547","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}