{"paper":{"title":"Extensions of algebraic groups with finite quotient and nonabelian 2-cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.GR","authors_text":"Giancarlo Lucchini Arteche","submitted_at":"2015-03-23T10:09:53Z","abstract_excerpt":"For a finite smooth algebraic group $F$ over a field $k$ and a smooth algebraic group $\\bar G$ over the separable closure of $k$, we define the notion of $F$-kernel in $\\bar G$ and we associate to it a set of nonabelian 2-cohomology. We use this to study extensions of $F$ by an arbitrary smooth $k$-group $G$. We show in particular that any such extension comes from an extension of finite $k$-groups when $k$ is perfect and we give explicit bounds on the order of these finite groups when $G$ is linear. We prove moreover some finiteness results on these sets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06582","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"}