Cambridge Journal of Mathematics

Volume 12 (2024)

Number 1

$p$-adic shtukas and the theory of global and local Shimura varieties

Pages: 1 – 164

DOI: https://dx.doi.org/10.4310/CJM.2024.v12.n1.a1

Authors

Georgios Pappas (Department of Mathematics, Michigan State University, East Lansing, Mich., U.S.A.)

Michael Rapoport (Mathematisches Institut der Universit¨at Bonn, Germany; and Department of Mathematics, University of Maryland, College Park, Md., U.S.A.)

Abstract

We establish basic results on p-adic shtukas and apply them to the theory of local and global Shimura varieties, and on their interrelation. We construct canonical integral models for (local, and global) Shimura varieties of Hodge type with parahoric level structure.

Keywords

Shimura variety, shtuka, integral model

2010 Mathematics Subject Classification

11G18, 14G35

Full Text (PDF format)

Georgios Pappas was partially supported by NSF grant DMS-2100743.

Received 19 July 2022

Published 30 January 2024