{"paper":{"title":"Bounding extensions for finite groups and Frobenius kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Brian J. Parshall, Christopher P. Bendel, Cornelius Pillen, Daniel K. Nakano, David I. Stewart, Leonard L. Scott","submitted_at":"2012-08-30T23:14:08Z","abstract_excerpt":"Let G be a simple, simply connected algebraic group defined over an algebraically closed field k of positive characteristic p. Let \\sigma:G->G be a strict endomorphism (i. e., the subgroup G(\\sigma) of \\sigma-fixed points is finite). Also, let G_\\sigma\\ be the scheme-theoretic kernel of \\sigma, an infinitesimal subgroup of G. This paper shows that the degree m cohomology H^m(G(\\sigma),L) of any irreducible kG(\\sigma)-module L is bounded by a constant depending on the root system \\Phi\\ of G and the integer m. A similar result holds for the degree m cohomology of G_\\sigma. These bounds are actua"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.6333","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":""},"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"}