2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98542Let X be a smooth variety over a field of characteristic p>0. We prove that the forgetful functor from the category of overconvergent F-isocrystals on X to the category of convergent F-isocrystals is fully faithful. The argument uses the quasi-unipotence theorem for overconvergent F-isocrystals (recently proved independently by Andre, Mebkhout, and the author; see math.AG/0110124), plus arguments of de Jong. In the process, we establish a theorem of Quillen-Suslin type (i.e., every finite projective module is free) over rings of overconvergent power series.18 pages; v4: second refereed version, adds overconvergent analogue of Quillen-Suslin. To appear in Geometric Aspects of Dwork's Theory (Dwork trimester proceedings)Algebraic Geometry12H25, 14F30text