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

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

2004-05-05

arxiv.org/abs/math/0405069v5

Mathematics

Number Theory

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

Scientific paper

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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