Finitude cohomologique des morphismes propres en g\'eom\'etrie   alg\'ebrique : une preuve transcendante sans techniques projectives
  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. 
Antoine Ducros