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arXiv · 0910.4434

Images directes II: F-isocristaux convergents

Jean-Yves Etesse
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Abstract

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.

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Jean-Yves Etesse. 2012-12-04. Images directes II: F-isocristaux convergents. https://arxiv.org/abs/0910.4434

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