  We 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 Geometry