Semistable reduction for overconvergent F-isocrystals, I: Unipotence and logarithmic extensions

2004/05/05 by Kiran S. Kedlaya, Kedlaya, Kiran S. · 1 citation
Mathematics · #14F30 #14F40 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:14F30 #msc:14F40

paper · pdf · doi:10.48550/arxiv.math/0405069

62 pages; v5: final refereed version; some corrected proofs in Section 3

arxiv created 2007/01/20 · arxiv updated 2009/12/01

Abstract

Let X be a smooth variety over a field of positive characteristic, and let E be an overconvergent isocrystal on X. We establish a criterion for the existence of a "canonical logarithmic extension" of E to a good compactification of X. In the process, we construct a category of overconvergent log-isocrystals and discuss its basic properties. In subsequent work, we will use these results to show that a canonical logarithmic extension always exists after pulling back E along a suitable cover of X.

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