Images directes I: Espaces rigides analytiques et images directes

Jean-Yves Etesse (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

This article is the first one of a series of three articles devoted to direct images of isocrystals: here we consider isocrystals without Frobenius structure; in the second one (resp. the third one ), we will introduce a Frobenius structure in the convergent (resp. overconvergent) context. For a liftable proper smooth morphism we establish the overconvergence of direct images, owing to a base change theorem for a proper morphism between rigid analytic spaces. This result partially answers a conjecture of Berthelot on the overconvergence of direct images under a proper smooth morphism.

Mots clés: isocristaux surconvergents; algèbres de Monsky-Washnitzer; schémas formels; espaces rigides analytiques; théorème de changement de base propre; cohomologie rigide; isocristaux surconvergents.

Domaines: Géométrie algébrique [math.AG]

Jean-Yves Etesse. Images directes I: Espaces rigides analytiques et images directes. Journal de Théorie des Nombres de Bordeaux, 2012, 24 (1), pp.101-151. ⟨hal-00425909v3⟩