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Berkeley Lectures on p-adic Geometry(AMS-207)$
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Peter Scholze and Jared Weinstein

Print publication date: 2020

Print ISBN-13: 9780691202082

Published to Princeton Scholarship Online: January 2021

DOI: 10.23943/princeton/9780691202082.001.0001

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Integral models of local Shimura varieties

Integral models of local Shimura varieties

Chapter:
(p.232) Lecture 25 Integral models of local Shimura varieties
Source:
Berkeley Lectures on p-adic Geometry
Author(s):

Peter Scholze

Jared Weinstein

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691202082.003.0025

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.

Keywords:   integral models, local Shimura varieties, Kudla-Rapoport-Zink, Rapoport-Zink spaces, PEL data, group-theoretic data, isomorphism, p-adic uniformization, Shimura curves, v-sheaves

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