Approches courantielles \`a la Mellin dans un cadre non archim\'edien

Abstract

We propose an approach of Mellin type for the approximation of integration currents or the effective realization of normalized Green currents associated with a cycle $ \bigwedge_1^m[{\rm div} (s_j)] $, where $s_j $ is a meromorphic section of a line bundle $ \mathscr{L}_j \rightarrow U$ over an open $U$ in a good Berkovich space when each $ \mathscr{L}_j$ has a smooth metric and $ {\rm codim}_{U}\big (\bigcap_{j \in J} {\rm Supp} [{\rm div (s_j)}] \big)\geq \# J$ for every set $ J \subset \{1, ..., p \} $. We also study the transposition to the non archimedean context of Crofton and King formulas, particularly the approximate realization of Vogel and Segre currents.