Formal moduli spaces of p-divisible groups in residue characteristic 2

• Applicant: Dr. Daniel Kirch
• Subject Area: Mathematics
• Term: from 2016 to 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 320227379

My project is part of the field of arithmetic algebraic geometry, more precisely it lies in the intersection of algebraic number theory, algebraic geometry and the theory of Shimura varieties. The objects of study are formal moduli spaces of p-divisible groups. These moduli spaces are defined by Rapoport and Zink. One application of these spaces is the uniformization of Shimura varieties and the study of their reduction, but their cohomology is also interesting in the context of local Langlands correspondences (cp. work of Fargues, Mantovan and Scholze).The definition by Rapoport and Zink includes moduli spaces of type EL (i.e. with extra data in form of endomorphisms and level structures) and of type PEL (like EL, with polarizations in addition) in the case p>2.The exclusion of residue characteristic 2 is a significant gap in this theory. A general definition (independent of the residue characteristic) would not only justify the theory of Rapoport-Zink spaces and their various (conjectural) generalizations (by Rapoport & Viehmann, Kim, Howard & Pappas), it is also essential for the study of special cycles on Shimura varieties in the context of the Kudla program.In my project I want to attempt a construction of such moduli spaces of type PEL in the case of residue characteristic 2. This project builds upon my PhD thesis, where I already defined a moduli spaces for a unitary group in two variables over a ramified quadratic extension. A first milestone would be the generalization of this result to unitary groups in more variables.

• DFG Programme: Research Fellowships
• International Connection: France
• Host: Professor Dr. Laurent Fargues