2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98546Let k be a field of characteristic p>0. A theorem of de Jong shows that morphisms of modules over W(k)[[t]] with Frobenius and connection structure descend from the completion of W(k)((t)). A careful reading of de Jong's proof suggests the possibility that an analogous theorem holds for modules with only a Frobenius structure. We show that this analogue holds in one weak formulation and fails in a second stronger formulation.18 pages; v2: corrected errors in Proposition 4.3 and Lemma 5.4; to appear in Math. Res. LettNumber TheoryAlgebraic GeometryRings and Algebras14F30; 13K05text