Notes on a Grothendieck–Serre conjecture in mixed characteristic case

Let $R$ be a discrete valuation ring with an infinite residue field, $X$ be a smooth projective curve over $R$. Let $\mathbf{G}$ be a simple simply-connected group scheme over $R$ and $E$ be a principal $\mathbf{G}$-bundle over $X$. We prove that $E$ is trivial locally for the Zariski topology on $X$ providing it is trivial over the generic point of $X$. The main aim of the present paper is to develop a method rather than to get a very strong concrete result.