Higher frames and $G$-displays

TL;DR

This paper extends the theory of displays to non-ordinary varieties of K3 type using $G$-structures, providing a new framework that generalizes existing deformation descriptions.

Contribution

It introduces a new approach to describe deformations of non-ordinary K3 type varieties via displays with $G$-structure, generalizing previous ordinary case methods.

Findings

Develops a modified definition of the tensor category of displays.

Extends the theory to non-ordinary varieties using $G$-displays.

Provides a framework similar to Fontaine-Jannsen's Frobenius gauges.

Abstract

Deformations of ordinary varieties of K3 type can be described in terms of displays by recent work of Langer-Zink. We extend this to the general (non-ordinary) case using displays with $G$-structure for a reductive group $G$. As a basis we suggest a modified definition of the tensor category of displays and variants which is similar to the Frobenius gauges of Fontaine-Jannsen.