The K-Theory Spectrum of Varieties
Abstract
Using a construction closely related to Waldhausen's S-construction, we produce a spectrum K(Var/k) whose components model the Grothendieck ring of varieties (over a field k) K0 (Var/k). We then produce liftings of various motivic measures to spectrum-level maps, including maps into Waldhausen's K-theory of spaces A() and to K(Q). We end with a conjecture relating K(Var/k) and the doubly-iterated K-theory of the sphere spectrum.
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