Mathematische Annalen

, Volume 330, Issue 4, pp 665–692 | Cite as

Weil-étale cohomology over finite fields

  • Thomas Geisser


We calculate the derived functors Rγ* for the base change γ from the Weil-étale site to the étale site for a variety over a finite field. For smooth and proper varieties, we apply this to express Tate’s conjecture and Lichtenbaum’s conjecture on special values of ζ-functions in terms of Weil-étale cohomology of the motivic complex ℤ(n).


Tate Finite Field Base Change Motivic Complex Proper Variety 
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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Thomas Geisser
    • 1
  1. 1.Department of MathematicsUniversity of Southern California, DRBLos AngelesUSA

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