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Prismatic $G$-displays and descent theory

Kazuhiro Ito

Vol. 19 (2025), No. 9, 1685–1770
Abstract

For a smooth affine group scheme G over the ring of p-adic integers p and a cocharacter μ of G, we study G-μ-displays over the prismatic site of Bhatt and Scholze. In particular, we obtain several descent results for them. If G = GL n, then our G-μ-displays can be thought of as Breuil–Kisin modules with some additional conditions. The relation between our G-μ-displays and prismatic F-gauges introduced by Drinfeld and Bhatt–Lurie is also discussed.

In fact, our main results are formulated and proved for smooth affine group schemes over the ring of integers 𝒪E of any finite extension E of p by using 𝒪E-prisms, which are 𝒪E-analogues of prisms.

Keywords
prisms, displays, $p$-divisible groups, prismatic $F$-gauges
Mathematical Subject Classification
Primary: 14F30
Secondary: 14G45, 14L05
Milestones
Received: 11 June 2023
Revised: 31 August 2024
Accepted: 18 October 2024
Published: 21 July 2025
Authors
Kazuhiro Ito
Mathematical Institute
Tohoku University
Sendai
Japan

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