Mathematische Zeitschrift

, Volume 269, Issue 1–2, pp 59–82 | Cite as

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

  • Atsushi ShihoEmail author


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 simple normal crossing divisor, under certain assumption. This is a p-adic analogue of a version of cut-by-curves criterion for regular singularity 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 ∇-modules.


Overconvergent isocrystal Solvability Highest ramification break Exponent 

Mathematics Subject Classification (2000)



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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Graduate School of Mathematical SciencesUniversity of TokyoTokyoJapan

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