Higher frames and G-displays

Abstract

Deformations of ordinary varieties of K3 type can be described in terms of displays, by recent work of Langer and Zink. We extend this to the general (nonordinary) case using displays with $G$-structure for a reductive group $G$. This is based on a modified definition of the tensor category of displays and variants of these which is related to the Frobenius gauges of Fontaine and Jannsen.