Central leaves and EKOR strata on Shimura varieties with parahoric reduction

• Main Author: Hesse, Jens
• Format: Others
• Language: en
• Published: 2020
• Online Access: https://tuprints.ulb.tu-darmstadt.de/11543/1/prom-official.pdf; Hesse, Jens <http://tuprints.ulb.tu-darmstadt.de/view/person/Hesse=3AJens=3A=3A.html> (2020): Central leaves and EKOR strata on Shimura varieties with parahoric reduction.Darmstadt, Technische Universität, DOI: 10.25534/tuprints-00011543 <https://doi.org/10.25534/tuprints-00011543>, [Ph.D. Thesis]

We investigate the geometry of the special fiber of the integral model of a Shimura variety with parahoric level at a given prime place. To be more precise, we deal with, firstly, the definition of central leaves in this situation, their local closedness, and the relationship between the folations for varying parahoric level. This is connected to the verification of axioms for integral models formulated by He and Rapoport. Secondly, we deal with the EKOR stratification which interpolates between the Ekedahl-Oort and Kottwitz-Rapoport stratifications. In the Siegel case we give a geometric description by suitably generalizing the theory of G-zips of Moonen, Wedhorn, Pink and Ziegler to our context.