Let Z → X be a nite branched Galois cover of normal projective geometrically integral varieties of dimension d ≥ 2 over a perfect eld 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 ...

Examples of knots and links distinguished by the total rank of their Khovanov homology but sharing the same two-fold branched cover are given. As a result, Khovanov homology does not yield an invariant of two-fold branched covers. Mutation provides an easy method for producing distinct knots sharing a common two-fold branched cover: The mutation in the branch set corresponds to a trivial surger...

We give a decomposition formula for the characteristic polynomials of ramified uniform covers of digraphs. Similarly, we obtain a decomposition formula for the characteristic polynomials of ramified regular covers of digraphs. As applications, we establish decomposition formulas for the characteristic polynomials of branched covers of digraphs and the zeta functions of ramified covers of digraphs.

We compute the stable reduction of some Galois covers of the projective line branched at three points. These covers are constructed using Hurwitz spaces parameterizing metacyclic covers. The reduction is determined by a certain hypergeometric differential equation. This generalizes the result of Deligne and Rapoport on the reduction of the modular curve X (p).