### A Chebotarev-type density theorem for divisors on algebraic varieties

**Holschbach, A ***(Pennsylvania)*

Tuesday 25 August 2009, 15:30-16:30

Seminar Room 1, Newton Institute

#### Abstract

Let Z/X be a finite branched Galois cover (with Galois group G) of normal, geometrically integral, projective varieties of dimension at least two over a field of characteristic zero. For each Weil prime divisor D on X, we can define the decomposition class C_D of D to be the conjugacy class of the decomposition group of any Weil prime divisor on Z mapping to D. Using the structure of the induced push-forward map on divisors, we derive density results on the set of prime divisors on X with a given decomposition class and explain some applications.