The triangulated category of K-motives DK_(k)

2013/02/08 by Garkusha, Grigory, Panin, Ivan
#Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1302.2163

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.

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