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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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Local Shimura varieties

Local Shimura varieties

(p.225) Lecture 24 Local Shimura varieties
Berkeley Lectures on p-adic Geometry

Peter Scholze

Jared Weinstein

Princeton University Press

This chapter specializes the theory back to the case of local Shimura varieties, and explains the relation with Rapoport-Zink spaces. It begins with a local Shimura datum. A local Shimura datum is a triple (G, b, µ) consisting of a reductive group G over Qp, a conjugacy class µ of minuscule cocharacters. Rapoport-Zink spaces are moduli of deformations of a fixed p-divisible group. After reviewing these, the chapter shows that the diamond associated with the generic fiber of a Rapoport-Zink space is isomorphic to a moduli space of shtukas of the form with µ minuscule. It then extends the results to general EL and PEL data.

Keywords:   local Shimura varieties, Rapoport-Zink spaces, local Shimura datum, minuscule cocharacters, p-divisible group, diamond, moduli space, shtukas, El data, PEL data

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