Images directes II: F-isocristaux convergents

Jean-Yves Etesse (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

This article is the second one of a series of three articles devoted to direct images of isocrystals: here we consider convergent isocrystals with Frobenius structure. Let V be a complete discrete valuation ring, with residue field k = V/m of characteristic p > 0 and fraction field K of characteristic 0. Firstly we characterize convergent F-isocrystals on a smooth affine k-scheme. Secondly, for perfect k and after a detailed exposition of the Teichmûller liftings, especially for the affine rigid line, we derive the existence of Frobenius isomorphisms on the direct images of convergent F-isocrystals under a proper smooth and liftable k-morphism.

Mots clés: F- isocristaux convergents; cohomologie cristalline; cohomologie convergente; cohomologie rigide; images directes.; images directes

Domaines: Géométrie algébrique [math.AG]

Jean-Yves Etesse. Images directes II: F-isocristaux convergents. 2009. ⟨hal-00425919v2⟩