Geodesic
On the Grothendieck--Serre conjecture concerning principal $G$-bundles over semi-local Dedekind domains
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 29, Tome 443 (2016), pp. 133-146

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Let $R$ be a semi-local Dedekind domain and let $K$ be the field of fractions of $R$. Let $G$ be a reductive semisimple simply connected $R$-group scheme such that every semisimple normal $R$-subgroup scheme of $G$ contains a split $R$-torus $\mathbb G_{m,R}$. We prove that the kernel of the map $$ H^1_{\unicode{x00E9}\unicode{x74}}(R,G)\to H^1_{\unicode{x00E9}\unicode{x74}}(K,G) $$ induced by the inclusion of $R$ into $K$, is trivial. This result partially extends the Nisnevich theorem [10, Thm.4.2]. 
@article{ZNSL_2016_443_a10,
     author = {I. A. Panin and A. K. Stavrova},
     title = {On the {Grothendieck--Serre} conjecture concerning principal $G$-bundles over semi-local {Dedekind} domains},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {133--146},
     publisher = {mathdoc},
     volume = {443},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_443_a10/}
}
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I. A. Panin; A. K. Stavrova. On the Grothendieck--Serre conjecture concerning principal $G$-bundles over semi-local Dedekind domains. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 29, Tome 443 (2016), pp. 133-146. http://geodesic.mathdoc.fr/item/ZNSL_2016_443_a10/