Morphisms of Berkovich analytic curves and the different function

יום ד', 10/12/2014 - 10:30

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.