Images directes I: Espaces rigides analytiques et images directes

Details Images directes I: Espaces rigides analytiques et images directes Images directes I: Espaces rigides analytiques et images directes

2009-10-23

arxiv.org/abs/0910.4433v3

Mathematics

Algebraic Geometry

57 pages

Scientific paper

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.

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