Strata and tautological classes for compactifications of Shimura varieties (C05)

• Subject Area: Mathematics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 444845124

The project aims to study the Ekedahl–Oort stratification on smooth projective toroidal compactifications of Shimura varieties of Hodge type in positive characteristic and their cycles classes in the tautological ring of a toroidal compactification. As an application, the objective is to obtain a description of the restriction of the tautological ring to the Shimura variety and to construct maximal projective subvarieties of Shimura varieties of Hodge type in positive characteristic. A further goal is to show that many interesting cycle classes, such as special cycles, those of Newton strata or those of central leaves, are also contained in the tautological ring, and to express them as linear combinations of cycle classes of Ekedahl–Oort strata. For this one extends the existing mod-p period maps to p-adic period maps. Finally, it is planned to extend results to the case of parahoric reductions.

• DFG Programme: CRC/Transregios
• Subproject of: TRR 326: Geometry and Arithmetic of Uniformized Structures (GAUS)
• Applicant Institution: Goethe-Universität Frankfurt am Main
• Project Head: Professor Dr. Torsten Wedhorn