2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59523We prove essential self-adjointness for semi-bounded below magnetic Schrödinger operators on complete Riemannian manifolds with a given positive smooth measure which is fixed independently of the metric. Some singularities of the scalar potential are allowed. This is an extension of the Povzner--Wienholtz--Simader theorem. The proof uses the scheme of Wienholtz but requires a refined invariant integration by parts technique, as well as a use of a family of cut-off functions which are constructed by a non-trivial smoothing procedure due to Karcher.24 pages, revised version, to appear in Journal of Functional AnalysisSpectral TheoryAnalysis of PDEs35P05, 58G25text