# The K-Theory Spectrum of Varieties

@article{Campbell2015TheKS,
title={The K-Theory Spectrum of Varieties},
author={Jonathan A. Campbell},
journal={arXiv: Algebraic Topology},
year={2015}
}
• Jonathan A. Campbell
• Published 2015
• Mathematics
• arXiv: Algebraic Topology
• Using a construction closely related to Waldhausen's $S_\bullet$-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 Waldhausen's $K$-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… CONTINUE READING

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