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

TL;DR

This paper applies Waldhausen's algebraic K-theory to motivic homotopy theory, revealing a connection between the Grothendieck ring of varieties and the algebraic K-theory of spaces over fields of characteristic zero.

Contribution

It introduces a novel application of algebraic K-theory machinery to motivic homotopy theory, establishing a surjective ring homomorphism from the Grothendieck ring to the path components.

Findings

Surjective ring homomorphism from Grothendieck ring to motivic homotopy components

New link between algebraic K-theory and motivic homotopy types

Application over fields of characteristic zero

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.