Cut-by-curves criterion for the log extendability of overconvergent isocrystals

Details Cut-by-curves criterion for the log extendability of overconvergent isocrystals Cut-by-curves criterion for the log extendability of overconvergent isocrystals

2009-06-24

arxiv.org/abs/0906.4381v1

Mathematics

Number Theory

25 pages

Scientific paper

In this paper, we prove a `cut-by-curves criterion' for an overconvergent isocrystal on a smooth variety over a field of characteristic $p>0$ to extend logarithmically to its smooth compactification whose complement is a strict normal crossing divisor, under certain assumption. This is a $p$-adic analogue of a version of cut-by-curves criterion for regular singuarity of an integrable connection on a smooth variety over a field of characteristic 0. In the course of the proof, we also prove a kind of cut-by-curves criteria on solvability, highest ramification break and exponent of $\nabla$-modules.

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