Closed orbits and reductive groups - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T17:40:45Z http://mathoverflow.net/feeds/question/44966 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/44966/closed-orbits-and-reductive-groups Closed orbits and reductive groups Ana 2010-11-05T16:40:17Z 2010-11-05T17:21:30Z <p>Let $G$ be a reductive algebraic group defined over a field $k$ and $X$ an affine $G$-variety.</p> <p>In the case $k$ is algebraically closed we have the following result:</p> <p>Let $x\in X$ such that the orbit $G\cdot x$ is closed, then the stabilizer $G_x$ is reductive.</p> <p>Is this result also valid for more general fields, as perfect fields?</p>