Descent of morphisms of overconvergent F-crystals

Details Descent of morphisms of overconvergent F-crystals Descent of morphisms of overconvergent F-crystals

2001-05-29

arxiv.org/abs/math/0105244v1

Mathematics

Algebraic Geometry

12 pages

Scientific paper

Tsuzuki has conjectured that for crystals with Frobenius and connection over a local field k((t)), the embedding of the category of overconvergent crystals into the category of convergent crystals is fully faithful. We prove Tsuzuki's conjecture restricted to the subcategory of potentially semistable (or quasi-unipotent) crystals, following de Jong's proof of a slightly weaker result. We also prove Tsuzuki's conjecture restricted to crystals with at most two distinct slopes.

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