The Shimurian BT stack is a gerbe over truncated displays

2025/10/27 by Lau, Eike
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2510.23207

Abstract

We show that the mod p fiber of the Shimurian stack BT_n^G,μ constructed by Gardner--Madapusi is a gerbe over the corresponding stack of truncated displays. This confirms a conjecture of Drinfeld.

Citations

• Ring stacks conjecturally related to the stacks BT_n^G,μ
• An algebraicity conjecture of Drinfeld and the moduli of p-divisible groups
• On the Lau group scheme
• On Shimurian generalizations of the stack BT₁⊗ F_p
• The prismatization of p-adic formal schemes
• Prismatization
• A Tannakian framework for G-displays and Rapoport-Zink spaces
• Topological Hochschild homology and integral p-adic Hodge theory
• Truncated Barsotti-Tate Groups and Displays
• Smoothness of the truncated display functor
• Frames and finite group schemes over complete regular local rings

Cited by

• Ring stacks conjecturally related to the stacks BT_n^G,μ

Related

• On Shimurian generalizations of the stack BT₁⊗ F_p
• A Note On Two Fiber Bundles and The Manifestations Of "Shtuka"
• The Nori fundamental gerbe of tame stacks
• Moduli of truncated shtukas and displays
• Ring stacks conjecturally related to the stacks BT_n^G,μ