most recent 30 from http://mathoverflow.net 2013-05-22T00:37:36Z http://mathoverflow.net/feeds/question/18633 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/18633/intersection-of-open-affines-is-affine Qfwfq 2010-03-18T18:20:31Z 2010-03-18T18:20:31Z

<p>I would like to see a clear, rigorous and elementary proof of the following statement:</p> <p>Let X be a (not necessary quasi-projective, separated) algebraic variety over the complex numbers, and let U,V be two affine open subsets of X. Then the intersection of U and V is affine.</p> <p>Does the proof change if one substitutes "scheme" for "variety"?</p>