Images directes III: F-isocristaux surconvergents

Details Images directes III: F-isocristaux surconvergents Images directes III: F-isocristaux surconvergents

2009-10-23

arxiv.org/abs/0910.4435v1

Mathematics

Algebraic Geometry

36 pages

Scientific paper

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.

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