2006/11/03 by Daniel Caro, Caro, Daniel
Mathematics · #14F30 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14F30
paper · pdf · doi:10.48550/arxiv.math/0611089
arxiv created 2006/11/03 · arxiv updated 2009/12/01
Let V be a mixed characteristic complete discrete valuation ring, k its residual field, P a proper smooth formal scheme over V, P its special fiber, T a divisor of P, U:=P∖ T, Y a smooth closed subscheme of U. We prove that the category of overconvergent F-isocrystals on Y is equivalent to the category of overcoherent F-isocrystals on Y. More generally, we prove such an equivalence by gluing for any smooth variety Y over k. Moreover, we check that overcoherent F-complexes of arithmetic D-modules split in overconvergent F-isocrystals.