Mathematische Zeitschrift

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

Motivic cohomology over Dedekind rings

  • Thomas Geisser


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.


Valuation Ring Smooth Variety Chow Group Discrete Valuation Ring Mixed Characteristic 
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© 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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