Purity for overconvergence

الأصل · EN

Let X 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 let Z Z X be closed subschemes of codimension at least 2. In this paper, we prove that the canonical restriction functor between the category of overconvergent F-isocrystals F- Isoc†(X,X) F- Isoc†(X Z, X Z) is an equivalence of categories. We also prove an application to the category of p-adic representations of the fundamental group of X, which is a higher-dimensional version of a result of Tsuzuki.