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

• Uwe Jannsen
Conference paper
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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