A^1-representability of hermitian K-theory and Witt groups, by Jens Hornbostel

We show that hermitian K-theory and Witt groups are representable both in the unstable and in the stable A^1-homotopy category of Morel and Voevodsky. In particular, Balmer Witt groups can be nicely expressed as homotopy groups of a topological space. The consequences include new results related to the projective line, blow ups and homotopy purity. Moreover, this will hopefully become part of a proof of Morel's conjecture on certain A^1-homotopy groups of spheres, saying in particular that the endomorphism ring of the motivic sphere spectrum in the stable A^1-homotopy category should be isomorphic to the Grothendieck-Witt ring of the base field.


Jens Hornbostel <jens.hornbostel@mathematik.uni-regensburg.de>