Morphisms of Berkovich analytic curves and the different function
In this talk we will study the topological ramification locus of a generically étale morphism f : Y --> X between quasi-smooth Berkovich curves. We define a different function \delta f : Y --> [0,1] which measures the wildness of the morphism. It turns out to be a piecewise monomial function on the curve, satisfying a balancing condition at type 2 points analogous to the classical Riemann-Hurwitz formula. We also explain how \delta can be used to explicitly construct the simultaneous skeletons of X and Y.
Joint work with Prof. M. Temkin and Dr. D. Trushin.
The talk will begin with a quick background on Berkovich curves. All terms will be defined.