Oliver Röndigs: The slices of Hermitian K-theory (Lecture 2)

The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "Workshop: Hermitian K-theory and trace methods"

Voevodsky constructed a filtration on the motivic stable homotopy category by measuring how many (de)suspensions with respect to the Tate circle are required to build a given motivic spectrum. The slices (i.e. the associated graded with respect to this filtration) of several motivic spectra (the motivic Eilenberg-MacLane spectrum, algebraic bordism, algebraic K-theory, the sphere spectrum) have been determined in work of Voevodsky, Levine, and others. In joint work with Paul Arne Ostvaer, we compute the slices of hermitian K-theory a.k.a. higher Grothendieck-Witt theory. One application is a quite natural approach to Milnor's conjecture on quadratic forms.