Local canonical heights for Galois covers of the projective line

Abstract We consider Galois covers of the projective line over a number field which are totally ramified above infinity. To this set-up we associate local canonical Weil heights at all places of the number field, generalizing the usual local Neron-Tate heights for elliptic curves. We will see that global invariants of such Galois covers can be naturally expressed using these local heights. Explicit limit formulas for the local heights will be discussed. The constructions make use of Berkovich spaces to deal with the non-archimedean places.