User peter - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T23:57:13Z http://mathoverflow.net/feeds/user/28151 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/113808/group-action-on-brauer-severi-varieties Group action on Brauer-Severi varieties Peter 2012-11-19T08:34:54Z 2012-11-19T08:34:54Z <p>Let X be a Brauer-Severi variety over k. I have understand that the automorphism scheme Aut_{X/k}=G as a group scheme acts on X via (m,pr_2):GxX /rightarrow XxX (multiplication morphism) and that this morphism is surjectiv. </p> <p>But what is about the action of Aut_{X/k}(k) on X?</p> <p>Is there for example a transitiv action of Aut_{X/k}(k) on the closed points of X?</p> <p>Or what kind of assumption is needed to get this?</p> http://mathoverflow.net/questions/112567/automorphism-group-on-brauer-severi-variety Automorphism Group on Brauer-Severi variety Peter 2012-11-16T11:04:44Z 2012-11-18T11:26:27Z <p>Let X be a Brauer-Severi variety over k, i.e. a variety that becomes isomorphic to the projective space after base change to a Galois-field extension of k.</p> <p>Does the automorphism group Aut(X) act on X transitivelly? </p> <p>Is there any literature about the action of Aut(X) on X?</p> http://mathoverflow.net/questions/113808/group-action-on-brauer-severi-varieties Comment by Peter Peter 2012-11-19T09:13:31Z 2012-11-19T09:13:31Z So suppose there are closed points x and y such that the residue fields are isomorphis as k-algebras does there exsist an element of Aut_{X/k}(k) mapping x to y? http://mathoverflow.net/questions/113808/group-action-on-brauer-severi-varieties Comment by Peter Peter 2012-11-19T08:56:41Z 2012-11-19T08:56:41Z I see, but supposing this is the case what can we say? http://mathoverflow.net/questions/112567/automorphism-group-on-brauer-severi-variety Comment by Peter Peter 2012-11-16T13:10:02Z 2012-11-16T13:10:02Z concretely: you have a closed point x in X and a closed point y in X, so is there an automorphism of X such that the automorphism maps x to y? http://mathoverflow.net/questions/112567/automorphism-group-on-brauer-severi-variety Comment by Peter Peter 2012-11-16T13:00:34Z 2012-11-16T13:00:34Z I was thinking on something in the sense of transitivity on the closed points of X. So we can consider a finite non split field extension of k, say L, and ask for the transitivity of Aut(X(L))-action on X(L).