Alexander Vishik (Nottingham)
Classification of Torsers and Subtle Stiefel-Whitney classes

(This is a joint work with Alexander Smirnov.) I will describe a new homotopic approach to the classification of torsers of algebraic groups. We work in the A^1-homotopy category of Morel-Voevodsky. In the case of the orthogonal group O(n), we introduce new invariants: ``Subtle Stiefel-Whitney classes'' which are much more informative than the classical ones (defined by J.Milnor). These invariants distinguish the triviality of the torser (quadratic form), see powers I^n of the fundamental ideal, contain Arason and higher invariants, and are related to the J-invariant of quadrics (thus, connecting previously isolated areas). These classes are also essential for the motivic description of the quadratic torser and of the highest quadratic Grassmannian.