Leaves in parahoric reductions of Shimura varieties

• Applicant: Professor Dr. Torsten Wedhorn
• Subject Area: Mathematics
• Term: from 2016 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 317095975

• Final Report Year: 2020

Final Report Abstract

Shimura varieties and their different variants play a central role in modern arithmetic geometry. This is well demonstrated not least by the fact that on every ICM in the last 25 years at least one fields medal was rewarded within this area. To apply their geometric properties to arithmetic problems one usually has to study their geometry modulo prime numbers. Already the existence of such geometric objects is a highly nontrivial fact that has been shown to hold in great generality by Kisin and Pappas. The standard technique to study these geometric objects modulo a prime is by stratifying them. An axiomatic frame work for these stratifications was set up by He and Rapoport. They also formulated many conjectures about these strata. In the project, Jens Hesse, supervised by me, proved many of these conjectures. This is a huge process in the theory of reductions of Shimura varieties.

Publications

• Central leaves on Shimura varieties with parahoric reduction, 2020, 43 pages
  Jens Hesse
  
• EKOR strata on Shimura varieties with parahoric reduction, 2020, 48 pages
  Jens Hesse