Geodesic
Notes on a Grothendieck--Serre conjecture in mixed characteristic case
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 35, Tome 484 (2019), pp. 138-148

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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. 
@article{ZNSL_2019_484_a9,
     author = {I. Panin},
     title = {Notes on a {Grothendieck--Serre} conjecture in mixed characteristic case},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {138--148},
     publisher = {mathdoc},
     volume = {484},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_484_a9/}
}
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I. Panin. Notes on a Grothendieck--Serre conjecture in mixed characteristic case. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 35, Tome 484 (2019), pp. 138-148. http://geodesic.mathdoc.fr/item/ZNSL_2019_484_a9/