2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68165In this article we compare different conditions on abelian schemes with real multiplication which occur in the integral models of the Hilbert-Blumenthal Shimura variety considered by Rapoport, Deligne, Pappas and Kottwitz. We show that the models studied by Deligne/Pappas and Kottwitz are isomorphic over Spec Z_(p). We also examine the associated local models and prove that they are equal.33 pages, LaTeX, some typos corrected, to appear in Journal of the Inst. of Math. Jussieu, Cambridge University PressAlgebraic Geometry14G35;11G18, 14K10 (14K15,11G10)text