Height 1 Group Schemes and Prismatic F-Gauges

We describe the prismatic F-gauge associated to a finite flat height one group scheme over a smooth variety of positive characteristic. As applications, we derive the description of the crystalline Dieudonné module of Berthelot-Breen-Messing in this case and recover results of Bragg-Olsson describing flat cohomology using a Hoobler-type sequence.