Motivic Cohomology, Localized Chern Classes, and Local Terms
نویسنده
چکیده
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` → c2Q` 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.
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