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-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.