Introduced in 1996, Rapoport-Zink spaces have since had an enormous impact in number theory and the Langlands program. They are moduli spaces that parametrize deformations of p-divisible groups, and thus are intimately linked to Shimura varieties. This is the content of the celebrated p-adic uniformization theorem of Rapoport and Zink, which describes local charts of Shimura varieties in terms of Rapoport-Zink spaces, and which formally looks very similar to the complex uniformization of a Shimura variety in terms of a Hermitian symmetric domain. Apart from that, Rapoport-Zink spaces also come into play when constructing local Shimura varieties, whose cohomology is supposed to realize local Langlands correspondences.
In this Kleine AG, which took place on the 18th of April 2026, we focused on constructing Rapoport-Zink spaces and proving the p-adic uniformization theorem. More information can be found in this announcement, as well as a more detailed syllabus for the talks. The next Kleine AG will be organized by Carlo Kaul and will revolve around the isomorphism of the Lubin-Tate and Drinfeld tower, as well as the p-adic Jacquet-Langlands correspondence.
The following was the schedule of the Kleine AG:
10:00 - 10:15: Arrival and Introduction
10:15 - 11:15: p-divisible groups and their (iso)crystals (Luozi Shi)
11:30 - 12:30: The Siegel setup (Carlo Kaul)
12:30 - 14:30: Lunch break and discussion of next Kleine AG
14:30 - 15:30: Representability of Rapoport-Zink spaces (Paul Philippe)
15:45 - 16:45: Local models and Weil descent (Tomáš Perutka)
17:00 - 18:00: The p-adic uniformization theorem (Fabian Schnelle)