Non-archimedean Green currents for the zero-locus of a regular section

We extend on the work of Bloch, Gillet, Soulé on non-archimedean Arakelov geometry, by proving in this context explicit formulas for Green currents, which are analogs of known formulas in complex geometry. More specifically, we prove an analog of the Poincaré-Lelong formula, as well as an equivalent of a formula by Bost, Gillet, Soulé, which expresses a Green current for the zero-locus of a regular section of a vector bundle. As corollaries, we also obtain non-archimedean counterparts of Levine formula and Martinelli formula.