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Mathematische Zeitschrift

, Volume 248, Issue 4, pp 773–794 | Cite as

Motivic cohomology over Dedekind rings

  • Thomas Geisser
Article

Abstract.

We study properties of Bloch’s higher Chow groups on smooth varieties over Dedekind rings. We prove the vanishing of Open image in new window for i > n, and the existence of a Gersten resolution for Open image in new window if the residue characteristic is p. We also show that the Bloch-Kato conjecture implies the Beilinson-Lichtenbaum conjecture Open image in new window an identification Open image in new window for m invertible, and a Gersten resolution with (arbitrary) finite coefficients. Over a complete discrete valuation ring of mixed characteristic (0,p), we construct a map from motivic cohomology to syntomic cohomology, which is a quasi-isomorphism provided the Bloch-Kato conjecture holds.

Keywords

Valuation Ring Smooth Variety Chow Group Discrete Valuation Ring Mixed Characteristic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Thomas Geisser
    • 1
  1. 1.Department of MathematicsKAP108, University of Southern CaliforniaLos AngelesUSA

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