K-THEORY AND MOTIVIC COHOMOLOGY OF SCHEMES, I

@inproceedings{LevineKTHEORYAM,
  title={K-THEORY AND MOTIVIC COHOMOLOGY OF SCHEMES, I},
  author={Marc A. Levine}
}
We examine the basic properties satisfied by Bloch’s cycle complexes for quasi-projective varieties over a field, and extend most of them to the cycle complex of a scheme of finite type over a regular dimension one base. We also extend these properties to the simplicial spectra in the homotopy niveau tower of the cosimplicial scheme ∆∗ X . As applications, we show that the homotopy coniveau spectral sequence from motivic cohomology to Ktheory is functorial for smooth schemes, admits a… CONTINUE READING

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