2009/10/23 by Jean-Yves Etesse, Etesse, Jean-Yves
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG
paper · pdf · doi:10.48550/arxiv.0910.4433
57 pages
arxiv created 2010/11/08 · arxiv updated 2010/11/09
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.