most recent 30 from http://mathoverflow.net 2013-05-24T22:50:54Z http://mathoverflow.net/feeds/question/62744 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/62744/is-every-reductive-group-scheme-etale-locally-trivial Roman Fedorov 2011-04-23T13:59:13Z 2011-04-29T11:24:29Z

<p>Let $S$ be a scheme over a field $k$, and let $G$ be a reductive group scheme over $S$. Let us call it <em>trivial</em>, if it is a pull-back of a group scheme over $k$ via the structure morphism $S\to k$. Is it always true that $G$ becomes trivial after a certain etale base change $S'\to S$? I am willing to assume that $S$ is smooth if needed.</p>

http://mathoverflow.net/questions/62744/is-every-reductive-group-scheme-etale-locally-trivial/63401#63401 Victor Petrov 2011-04-29T11:24:29Z 2011-04-29T11:24:29Z

<p>Reductive groups schemes over $S$ are classified by $H^1_{fpqc}(S,Aut_G)$, see SGA 3 Exp. XXIV.</p>