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Techniques of localization in the theory of algebraic cycles. (English) Zbl 1077.14509

Summary: We extend the localization techniques developed hy Bloch to simplicial spaces. As applications, we give an extension of Bloch’s localization theorem for the higher Chow groups to schemes of finite type over a regular scheme of dimension at most one (including mixed characteristic) and, relying on a fundamental result of Friedlander and Suslin, we globalize the Bloch-Lichtenbaum spectral sequence to give a spectral sequence converging to the \(G\)-theory of a scheme \(X\), of finite type over a regular scheme of dimension one, with \(E^1\)-term the motivic Borel-Moore homology.

MSC:

14C25 Algebraic cycles
14F42 Motivic cohomology; motivic homotopy theory
19E15 Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects)
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