2010/07/20 by Atsushi Shiho, Shiho, Atsushi
Mathematics · #12F25 #14F35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #math.AG #math.NT #msc:12F25 #msc:14F35
paper · pdf · doi:10.48550/arxiv.1007.3345
22 pages
arxiv created 2010/07/20 · openalex publication_date 2010/07/20 · arxiv updated 2010/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X \hookrightarrow 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-\rm Isoc†(X,X) \longrightarrow F-\rm 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.