Saturday, February 25, 2006

Ol' Brauer

I ran across "The flat locus of Brauer-Severi fibrations of smooth orders" today. It reminded me of a problem I once found very interesting:

Given a quasi-compact separated scheme X, is Br(X) = H2(X,Gm)tors? There are some examples of non-separated (but even semi-separated) schemes for which this is not true.