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The K-Theory Spectrum of Varieties

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 Added by Jonathan Campbell
 Publication date 2015
  fields
and research's language is English




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Using a construction closely related to Waldhausens $S_bullet$-construction, we produce a spectrum $K(mathbf{Var}_{/k})$ whose components model the Grothendieck ring of varieties (over a field $k$) $K_0 (mathbf{Var}_{/k})$. We then produce liftings of various motivic measures to spectrum-level maps, including maps into Waldhausens $K$-theory of spaces $A(ast)$ and to $K(mathbf{Q})$. We end with a conjecture relating $K(mathbf{Var}_{/k})$ and the doubly-iterated $K$-theory of the sphere spectrum.



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