Descente fid\`element plate et alg\'ebrisation en g\'eom\'etrie de Berkovich

Abstract

This article studies descent theory in the setting of Berkovich spaces. We give sufficient conditions for a given fibered category over the category of k-affinoid algebras to be a stack for the Berkovich analogue of the faithfully-flat topology. We give some applications to the faithfully flat descent of morphisms and show that some descent data are always effective. We also show that the property of being algebraic for a morphism between the analytification of two schemes is a local property for the faithfully-flat topology.