Finiteness of fppf cohomology

Abstract

Let $R$ be a Henselian DVR with finite residue field. Let $G$ be a finite type, flat $R$-group scheme (not necessarily commutative) with smooth generic fiber. We show that $H^1_{\mathrm{fppf}}(\mathrm{Spec} R,G)$ is finite. We then give an application of the global analogue of this finiteness result to PEL type integral models of Shimura varieties.