  Let $Z \to X$ be a finite branched Galois cover of normal projective
geometrically integral varieties of dimension $d \geq 2$ over a perfect field
$k$. For such a cover, we prove a Chebotarev-type density result describing the
decomposition behaviour of geometrically integral Cartier divisors. As an
application, we classify Galois covers among all finite branched covers of a
given normal geometrically integral variety $X$ over $k$ by the decomposition
behaviour of points of a fixed codimension $r$ with $0 < r < \dim X$.
