3.30 p.m., Seminar Hall
Harder-Narasimhan schemes and stacks
We show that in characteristic zero, for any family of principal bundles in higher diemsions with a reductive structure group, there is a schematic stratification of the base, given by Harder-Narasimhan types. In positive characteristic, where (infinitesimal) uniqueness of reduction can fail, we can still show the existence of a universal scheme of reductions. As a corollary, in all dimensions and in all characteristics, principal bundles of a given Harder-Narasimhan type form an algebraic stack. (Joint work with Sudarshan Gurjar).