MOTIVIC COHOMOLOGY, LOCALIZED CHERN CLASSES, AND LOCAL TERMS

Abstract

Abstract. Let c: C → X×X be a correspondence with C and X quasi-projective schemes over an algebraically closed field k. We show that if u ` : c 1Q ` → c!2Q ` is an action defined by the localized Chern classes of a c2-perfect complex of vector bundles on C, where ` is a prime invertible in k, then the local terms of u ` are given by the class of an algebraic cycle independent of `. We also prove some related results for quasi-finite correspondences. The proofs are based on the work of Cisinski and Deglise on triangulated categories of motives. Content