Images directes III: F-isocristaux surconvergents

Jean-Yves Etesse (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

This article is the third one of a series of three articles devoted to direct images of isocrystals: here we consider overconvergent isocrystals with Frobenius structure. For a liftable proper smooth morphism we establish the overconvergence of direct images, owing to the first article and the existence of lifts of Frobenius. This result partially answers a conjecture of Berthelot on the overconvergence of direct images of overconvergent F-isocrystals under a proper smooth morphism.

Mots clés: images directes; algèbres de Monsky-Washnitzer; schémas formels; espaces rigides analytiques; F- isocristaux surconvergents; cohomologie rigide; images directes.

Domaines: Géométrie algébrique [math.AG]

Jean-Yves Etesse. Images directes III: F-isocristaux surconvergents. 2009. ⟨hal-00425922⟩