Morphisms of Berkovich analytic curves and the different function

Wed, 10/12/2014 - 10:30
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Abstract: 

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.