Kottwitz-Rapoport strata in the Siegel moduli spaces
This paper provides a survey of various results concerning Siegel moduli spaces with parahoric level structures and Kottwitz-Rapoport (KR) stratification. The author describes the supersingular locus of the Siegel 3-folds with parahoric structures of paramodular type and Klingen type and discusses how to characterize the KR strata in the moduli spaces with Iwahori level structure. He also announces additional results on the KR strata in Siegel 3-folds with parahoric level structure and those in higher dimensional cases, whose proofs will be given in subsequent papers with U.~Görtz. These results include a numerical characterization for KR strata, a method of reducing certain geometric problems to those on \(p\)-rank zero strata, and a description of the supersingular KR structure in the genus three case.
scientific article; zbMATH DE number 5896863