In this talk I will introduce subtle characteristic classes for Hermitian forms, which come from the motivic cohomology ring of the Nisnevich classifying space of the unitary group associated to the standard split Hermitian form of a quadratic extension. Moreover, I will relate these new invariants to subtle Stiefel-Whitney classes introduced by Smirnov and Vishik and deduce information on the kernel invariant of quadratic forms divisible by a 1-fold Pfister form. Finally, I will show that these invariants see the triviality of Hermitian forms and present the motive of the torsor associated to a Hermitian form in terms of its subtle characteristic classes.
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- Oberseminar: Motivische algebraische Topologie