The Grothendieck ring of varieties and algebraic K-theory of spaces

Abstract

Waldhausen's algebraic K-theory machinery is applied to motivic homotopy theory, producing an interesting motivic homotopy type. Over a field F of characteristic zero, its path components receive a surjective ring homomorphism from the Grothendieck ring of varieties over F.

arXiv comment31 pages. Almost identical to the version to be published in: The Open Book Series - Motivic Geometry (Oslo)

References in corpus (6)

• Triangulated categories of mixed motives
• A universal characterization of higher algebraic K-theory
• Cancellation theorem
• The smooth Whitehead spectrum of a point at odd regular primes
• Differential graded motives: weight complex, weight filtrations and spectral sequences for realizations; Voevodsky vs. Hanamura
• On some finiteness results in real étale cohomology

Cited by in corpus (5)

• Künneth formulas for motives and additivity of traces
• Compactly supported ${\mathbb{A}}^1$-Euler characteristic and the Hochschild complex
• From Six Functors Formalisms to Derived Motivic Measures
• Compactly supported ${\mathbb{A}}^1$-Euler characteristics of symmetric powers of cellular varieties
• Equivariant motivic Hall algebras