The triangulated category of K-motives DK_(k)

TL;DR

This paper constructs a triangulated category of K-motives over perfect fields, linking it to Quillen's K-theory and extending Voevodsky's framework for motives.

Contribution

It introduces a new triangulated category of K-motives for perfect fields, connecting K-theory with motivic categories in the style of Voevodsky.

Findings

K-motives are associated to smooth k-varieties

K_n(X) is represented by Hom in DK_(k)

The construction generalizes existing motivic frameworks

Abstract

For any perfect field k a triangulated category of K-motives DK_(k) is constructed in the style of Voevodsky's construction of the category DM_(k). To each smooth k-variety X the K-motive is associated in the category DK_(k). Also, it is shown that K_n(X)=DK_(k)(M_K(X)[n],M_K(pt)), where K(X) is Quillen's K-theory of X.