Levine, Marc Techniques of localization in the theory of algebraic cycles. (English) Zbl 1077.14509 J. Algebr. Geom. 10, No. 2, 299-363 (2001). 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. Cited in 4 ReviewsCited in 37 Documents MSC: 14C25 Algebraic cycles 14F42 Motivic cohomology; motivic homotopy theory 19E15 Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects) PDFBibTeX XMLCite \textit{M. Levine}, J. Algebr. Geom. 10, No. 2, 299--363 (2001; Zbl 1077.14509)