2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63964This is a report on results and methods in the reduction modulo p of Shimura varieties with parahoric level structure. In the first part, the local theory, we explain the concepts of parahoric subgroups, of the mu-admissible and mu-permissible subsets of the Iwahori-Weyl group, of the corresponding union of affine Deligne-Lusztig varieties and of local models. In the second part, the global theory, we use these concepts to formulate conjectures on the points in the reduction modulo p of Shimura varieties with parahoric level structure.AMS-TeX, 40 pagesAlgebraic Geometry14G35; 11G18text