Height 1 Group Schemes and Prismatic F-Gauges

TL;DR

This paper explores the structure of height one group schemes via prismatic F-gauges, linking to crystalline Dieudonné modules and flat cohomology, advancing understanding in algebraic geometry over positive characteristic fields.

Contribution

It introduces a new description of prismatic F-gauges for height one group schemes and connects it to existing theories like Dieudonné modules and flat cohomology.

Findings

Describes prismatic F-gauge for height one group schemes.

Derives the crystalline Dieudonné module in this context.

Recovers results on flat cohomology using Hoobler-type sequences.

Abstract

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 Dieudonn\'e module of Berthelot-Breen-Messing in this case and recover results of Bragg-Olsson describing flat cohomology using a Hoobler-type sequence.