# Lifting harmonic morphisms I: metrized complexes and Berkovich skeleta

@article{Amini2013LiftingHM,
title={Lifting harmonic morphisms I: metrized complexes and Berkovich skeleta},
author={Omid Amini and Matthew Baker and Erwan Brugall{\'e} and Joseph Rabinoff},
journal={Research in the Mathematical Sciences},
year={2013},
volume={2},
pages={1-67}
}
• Published 20 March 2013
• Mathematics
• Research in the Mathematical Sciences
Let K be an algebraically closed, complete non-Archimedean field. The purpose of this paper is to carefully study the extent to which finite morphisms of algebraic K-curves are controlled by certain combinatorial objects, called skeleta. A skeleton is a metric graph embedded in the Berkovich analytification of X. A skeleton has the natural structure of a metrized complex of curves. We prove that a finite morphism of K-curves gives rise to a finite harmonic morphism of a suitable choice of…
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