Admissible metrics for line bundles on curves and abelian varieties over non-archimedean local fields

Abstract

Following the approach in the archimedean case, we introduce the notion of admissible metrics for line bundles on curves and abelian varieties over non-archimedean local fields. Several properties of admissible metrics are considered and we show that this approach yields the same notion of admissible metrics over curves as doing harmonic analysis on the reduction graph of the curve.