The different for base change of arithmetic curves

We introduce a method for studying reduction types of arithmetic curves and wildly ramified base change. We give new proofs of earlier results of Lorenzini and Obus-Wewers, and resolve a question of Lorenzini on the Euler characteristic of the resolution graph of a $p$-cyclic arithmetic surface quotient singularity. Our method consists of constructing a simultaneous skeleton for the associated cover of Berkovich analytifications and applying a skeletal Riemann-Hurwitz formula.