2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120189We propose here a transcendantal proof of the coherence of the higher direct images of a coherent sheaf by a proper morphism of algebraic varieties, which does not use Chow's lemma nor any projective method. The main tool here are comparison with coherent cohomology of a (Berkovich) analytic space over a trivially valued field, and Kiehls' theorem about the proper morphisms between rigid-analytic spaces.Algebraic Geometry14A15, 14F99text