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On the ℓ-adic cohomology of varieties over number fields and its Galois cohomology

  • Uwe Jannsen
Part of the Mathematical Sciences Research Institute Publications book series (MSRI, volume 16)

Abstract

If X is a smooth, projective variety over a number field k, then the absolute Galois group Gk = Gal(/k) acts on the étale cohomology groups Hi(, ℚ/ℤ(n)), where = X Xk for an algebraic closure of k. In this paper I study some properties of these Gk-modules; in particular, I am interested in the corank of the Galois cohomology groups
$${H^v}\,({G_k},{H^i}(\bar X,\,{Q_\ell }/{Z_\ell }(n))).$$

Keywords

Exact Sequence Abelian Variety Chern Class Number Field Good Reduction 
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 New York Inc. 1989

Authors and Affiliations

  • Uwe Jannsen
    • 1
  1. 1.FB MathematikUniversität RegensburgRegensburgFederal Republic of Germany

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