Approches courantielles à la Mellin dans un cadre non archimédien

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 ${\bigwedge }_1^m[\mathrm{div}(s_j)]$, where $s_j$ is a meromorphic section of a line bundle ${\mathcal{L}}_j\to U$ over an open $U$ in a good Berkovich space when each ${\mathcal{L}}_j$ has a smooth metric and ${\mathrm{codim}}_U({\bigcap }_{j\in J}\mathrm{Supp}[\mathrm{div}({\mathrm{s}}_{\mathrm{j}})])\ge \#J$ 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.

arXiv commentin French