Let $S=\mathrm{Spec}(R)$, $s=\mathrm{Spec}(k)$ and $\eta=\mathrm{Spec}(K)$, where $R$ is a d.v.r. with fraction field $K$. Let $j:\eta\rightarrow S$


Now how to compute the sheaf $R^1j\_\*(\mathbb{G}\_{m,\eta})$ in the fppf topology?


The case for etale topology is zero by considering the stalks and use the Hilbert 90. 



How to compute the first derived direct image along an open immersion, for the fppf sheaf represented by a multiplicative group?
It seems to me that (equation) 5.2 and Appendice 11.7 of "Le Groupe de Brauer, III" imply that the cohomology for the \'etale topology equals the cohomology for the fppf topology. 


