The Shimurian BT stack is a gerbe over truncated displays

TL;DR

This paper proves that the mod p fiber of the Shimurian stack forms a gerbe over the stack of truncated displays, confirming a conjecture by Drinfeld, and deepening the understanding of the stack's structure.

Contribution

It establishes that the Shimurian stack's mod p fiber is a gerbe over truncated displays, confirming Drinfeld's conjecture and advancing the theory of algebraic stacks.

Findings

The mod p fiber of the Shimurian stack is a gerbe over truncated displays.

Confirmation of Drinfeld's conjecture on the structure of the Shimurian stack.

Enhanced understanding of the geometric properties of Shimurian stacks.

Abstract

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