Integral models of local Shimura varieties

Abstract

This chapter explains an application of the theory developed in these lectures towards the problem of understanding integral models of local Shimura varieties. As a specific example, it resolves conjectures of Kudla-Rapoport-Zink and Rapoport-Zink, that two Rapoport-Zink spaces associated with very different PEL data are isomorphic. The basic reason is that the corresponding group-theoretic data are related by an exceptional isomorphism of groups, so such results follow once one has a group-theoretic characterization of Rapoport-Zink spaces. The interest in these conjectures comes from the observation of Kudla-Rapoport-Zink that one can obtain a moduli-theoretic proof of Čerednik's p-adic uniformization for Shimura curves using these exceptional isomorphisms. The chapter defines integral models of local Shimura varieties as v-sheaves.