{"paper":{"title":"Second cohomology for finite groups of Lie type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Andrew J. Talian, Benjamin J. Wyser (University of Georgia VIGRE Algebra Group), Brandon L. Samples, Brian Bonsignore, Brian D. Boe, Christopher M. Drupieski, Daniel K. Nakano, Jon F. Carlson, Leonard Chastkofsky, Lisa Townsley, Nham Vo Ngo, Niles Johnson, Phong Thanh Luu, Theresa Brons, Tiago Macedo, Wenjing Li","submitted_at":"2011-10-02T20:32:16Z","abstract_excerpt":"Let $G$ be a simple, simply-connected algebraic group defined over $\\mathbb{F}_p$. Given a power $q = p^r$ of $p$, let $G(\\mathbb{F}_q) \\subset G$ be the subgroup of $\\mathbb{F}_q$-rational points. Let $L(\\lambda)$ be the simple rational $G$-module of highest weight $\\lambda$. In this paper we establish sufficient criteria for the restriction map in second cohomology $H^2(G,L(\\lambda)) \\rightarrow H^2(G(\\mathbb{F}_q),L(\\lambda))$ to be an isomorphism. In particular, the restriction map is an isomorphism under very mild conditions on $p$ and $q$ provided $\\lambda$ is less than or equal to a fun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0228","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":""},"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"}