2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/124449Let X be a scheme that does not satisfy the valuative criterion of separatedness. We show that the Hilbert functor parametrizing closed families of X that are flat, finite and of rank one is not represented by a scheme or an algebraic space.8 pages Changed abstract. Fixed typos/grammatical errors. Shortened the introduction. Expanded and clarified Remark 1.9. Shortened the exposition in Section 2 considerably, especially the proof of the first proposition (now Prop 2.3) in this section. Also removed the first lemma (Lemma 2.3) in the section. Added/removed referencesAlgebraic Geometry14C05 (Primary) 14B12, 14A20 (Secondary)text