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Canonical integral models for Shimura varieties of toral type

Patrick Daniels

Vol. 19 (2025), No. 2, 247–286
DOI: 10.2140/ant.2025.19.247
Abstract

We prove the Pappas–Rapoport conjecture on the existence of canonical integral models of Shimura varieties with parahoric level structure in the case where the Shimura variety is defined by a torus. As an important ingredient, we show, using the Bhatt–Scholze theory of prismatic F-crystals, that there is a fully faithful functor from 𝒢-valued crystalline representations of Gal (K¯K) to 𝒢-shtukas over Spd (𝒪K), where 𝒢 is a parahoric group scheme over p and 𝒪K is the ring of integers in a p-adic field K.

Keywords
integral models of Shimura varieties, shtukas
Mathematical Subject Classification
Primary: 11G18
Secondary: 14G45
Milestones
Received: 28 July 2022
Revised: 2 February 2024
Accepted: 29 March 2024
Published: 31 January 2025
Authors
Patrick Daniels
Department of Mathematics and Statistics
Skidmore College
Saratoga Springs, NY
United States

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