A Tannakian Framework for Displays and Rapoport-Zink Spaces
Files
Publication or External Link
Date
Authors
Advisor
Citation
DRUM DOI
Abstract
We develop a Tannakian framework for group-theoretic analogs of displays,
originally introduced by Bültel and Pappas, and further studied by Lau. We use
this framework to define Rapoport-Zink functors associated to triples (G, {μ}, [b]),
where G is a flat affine group scheme over Zp and μ is a cocharacter of G defined over
a finite unramified extension of Zp. We prove these functors give a quotient stack
presented by Witt vector loop groups, thereby showing our definition generalizes
the group-theoretic definition of Rapoport-Zink spaces given by Bültel and Pappas.
As an application, we prove a special case of a conjecture of Bültel and Pappas by
showing their definition coincides with that of Rapoport and Zink in the case of
unramified EL-type local Shimura data.