nLab Rapoport-Zink space

Idea

A Rapoport-Zink space is a formal scheme parametrizing deformations of a p-divisible group. They may be thought of as local analogs of Shimura varieties.

Related ideas

• Lubin-Tate space

References

• M. Rapoport, Th. Zink, Period spaces for $p$-divisible groups, Annals of Mathematics Studies, vol. 141, Princeton University Press, Princeton, NJ, 1996.

Review of the first three sections of (Rapoport-Zink 96) is in

• Rapoport-Zink spaces, lecture notes 2013 pdf

Further lecture notes include

• KIAS Intensive Lecture Series on Shimura varieties and Rapoport-Zink spaces (web)

Further developments include

• Peter Scholze, Jared Weinstein, Moduli of p-divisible groups (arXiv:1211.6357)

Comments on the relation to shtukas in view of the function field analogy are in

• Urs Hartl, A Dictionary between Fontaine-Theory and its Analogue in Equal Characteristic (arXiv:math/0607182)