The standard realizations for the K-theory of varieties

Higher Structures 2026 Open access

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Authors: Oliver Bräunling, Michael Groechenig, Anubhav Nanavaty
DOI: 10.21136/hs.2026.01
Cited by: 3
References: 14

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.

Fields of Study & Subjects

Algebraic Geometry and Number Theory Homotopy and Cohomology in Algebraic Topology Advanced Algebra and Geometry

Publication details

Journal / source
Higher Structures
Publisher
Institute of Mathematics, Czech Academy of Sciences
Volume
10
Issue
1
Pages
1–21
Publication date
19 June 2026
Language
EN