Selecta Mathematica

, Volume 17, Issue 4, pp 833–854 | Cite as

Purity for overconvergence

  • Atsushi ShihoEmail author


Let \({X \hookrightarrow \overline{X}}\) be an open immersion of smooth varieties over a field of characteristic p > 0 such that the complement is a simple normal crossing divisor and \({\overline{Z}\subseteq Z \subseteq \overline{X}}\) closed subschemes of codimension at least 2. In this paper, we prove that the canonical restriction functor between the categories of overconvergent F-isocrystals \({F-{\rm Isoc}^\dagger(X,\overline{X}) \longrightarrow F-{\rm Isoc}^\dagger(X{\setminus}Z, \overline{X}{\setminus}\overline{Z})}\) is an equivalence of categories. We also give an application of our result to the equivalence of certain categories.


Isocrystal Overconvergence Purity p-adic representation 

Mathematics Subject Classification (2010)

12H25 14F35 


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© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Graduate School of Mathematical SciencesUniversity of TokyoTokyoJapan

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