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The Shimurian BT stack is a gerbe over truncated displays

Eike Lau

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.

The Shimurian BT stack is a gerbe over truncated displays

Abstract

We show that the mod fiber of the Shimurian stack constructed by Gardner--Madapusi is a gerbe over the corresponding stack of truncated displays. This confirms a conjecture of Drinfeld.
Paper Structure (64 sections, 51 theorems, 133 equations)

This paper contains 64 sections, 51 theorems, 133 equations.

Table of Contents

  1. Introduction
  2. Main result
  3. Reduction to an elementary version
  4. Drinfeld's group scheme
  5. Sheared Witt vectors
  6. On the proof of Theorem \ref{['Th:Main-pre']}
  7. Outline
  8. Acknowledgements
  9. Frames and modules
  10. Frames
  11. Modules
  12. Ideals
  13. $(G,\mu)$-groupoids
  14. Preliminaries
  15. Definition of the groupoid
  16. ...and 49 more sections

Key Result

Theorem A

The morphism $\phi_n^{G,\mu}$ is a gerbe banded by the group scheme $\mathfrak{D}_n^{G,\mu}$.

Theorems & Definitions (121)

  • Theorem A
  • Theorem B
  • Theorem C
  • Remark 2.1
  • Definition 2.2
  • Definition 2.5
  • Remark 2.6
  • Example 2.7
  • Remark 2.8
  • Definition 2.9
  • ...and 111 more