A Chebotarev-type density theorem for divisors on algebraic varieties

Abstract

Let Z -> X be a finite branched Galois cover of normal projective
geometrically integral varieties of dimension d >- 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 nite 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 < dimX.