Proof of Borel-Weil-Bott Theorem - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T15:29:26Z http://mathoverflow.net/feeds/question/13657 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/13657/proof-of-borel-weil-bott-theorem Proof of Borel-Weil-Bott Theorem unknown (google) 2010-02-01T10:56:35Z 2010-03-22T19:39:02Z <p>Is there any purely algebraic proof of Borel-Weil-Bott theorem. I mean only techniques from Algebraic group. In each and every proof I have seen so far they use Lie group techniques and then translate to Algebraic group version. I need a proper reference which is easily readable.</p> <p>Thanks in advance.</p> http://mathoverflow.net/questions/13657/proof-of-borel-weil-bott-theorem/13667#13667 Answer by Marty for Proof of Borel-Weil-Bott Theorem Marty 2010-02-01T12:35:09Z 2010-02-01T12:35:09Z <p>Near the bottom of <a href="http://www.math.harvard.edu/~lurie/" rel="nofollow">Jacob Lurie's homepage</a>, you can find an exposition of the Borel-Weil-Bott theorem from an algebro-geometric standpoint. It is "easily readable" if you're familiar with the things like line bundles on projective varieties, semisimple algebraic groups, etc.. </p> http://mathoverflow.net/questions/13657/proof-of-borel-weil-bott-theorem/13694#13694 Answer by Kevin McGerty for Proof of Borel-Weil-Bott Theorem Kevin McGerty 2010-02-01T15:13:03Z 2010-02-01T15:13:03Z <p>The simplest proof of Borel-Weil-Bott that I know is due to Demazure: he has two papers in Inventiones (one in 1968 the other in 1976) on the theorem, and the second is two pages long -- it gives a simplification of his previous proof, and he uses only algebro-geometric techniques. Both papers are readable. </p> http://mathoverflow.net/questions/13657/proof-of-borel-weil-bott-theorem/19056#19056 Answer by George McNinch for Proof of Borel-Weil-Bott Theorem George McNinch 2010-03-22T19:39:02Z 2010-03-22T19:39:02Z <p>See J.C. Jantzen "Representations of Algebraic Groups" II.5 especially II.5.5. </p> <p>There you will find an algebraic proof of the result in char. 0 (probably more-or-less Demazure's proof, mentioned in another answer). And you'll find a proof of some of what remains true in positive char (due to Henning Anderson).</p>