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arXiv · 2606.19160

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

Léo Dubocs
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Abstract

We extend on the work of Bloch, Gillet, Soul\'e 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 Poincar\'e-Lelong formula, as well as an equivalent of a formula by Bost, Gillet, Soul\'e, 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.

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Léo Dubocs. 2026-06-17. Non-archimedean Green currents for the zero-locus of a regular section. https://arxiv.org/abs/2606.19160

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