A Chebotarev-type density theorem for divisors on algebraic varieties

Abstract

Let $Z\to X$ be a finite branched Galois cover of normal projective geometrically integral varieties of dimension $d\ge 2$ 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 $0<r<\dim X$.

Introduction reorganized, some other (minor) changes. 31 pages