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arXiv · 2107.01168

The standard realizations for the K-theory of varieties

Oliver Braunling·Michael Groechenig·Anubhav Nanavaty
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Abstract

The Grothendieck ring of varieties has well-known realization maps to, say, mixed Hodge structures or compactly supported $\ell$-adic cohomology. Zakharevich and\ Campbell have developed {a spectral refinement} of the Grothendieck ring of varieties. We develop a realization map to Voevodsky mixed motives, and this lifts the standard realizations of motives to this setting, at least over perfect fields which have resolution of singularities.

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Oliver Braunling, Michael Groechenig, Anubhav Nanavaty. 2021-07-02. The standard realizations for the K-theory of varieties. https://arxiv.org/abs/2107.01168

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