K-theory and Motivic Cohomology of Schemes
نویسنده
چکیده
We examine some of the basic properties satisfied by Bloch’s cycle complexes for quasi-projective varieties over a field, and extend some of them to the cycle complex of a scheme of finite type over a regular dimension one base. We also give an extension to the simplicial spectra in the niveau tower of the cosimplicial scheme ∆∗ X . As applications, we show that the AtiyahHirzebruch spectral sequence from motivic cohomology to K-theory admits a multiplicative structure, has Adams operations, and maps to a similar spectral sequence from étale cohomology to étale K-theory.
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