Images directes II: F-isocristaux convergents

Details Images directes II: F-isocristaux convergents Images directes II: F-isocristaux convergents

2009-10-23

arxiv.org/abs/0910.4434v1

Mathematics

Algebraic Geometry

39 pages

Scientific paper

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 tamely ramified V, we derive the convergence of direct images of (almost) all convergent F-isocrystals under a proper smooth k-morphism.

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