2009/10/23 by Jean-Yves Étesse, Jean-Yves Etesse, Etesse, Jean-Yves · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Finite Group Theory Research #math.AG
paper · pdf · doi:10.48550/arxiv.0910.4434
70 pages
arxiv created 2012/12/04 · arxiv updated 2012/12/05
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.