Geodesic
Two purity theorems and the Grothendieck-Serre conjecture concerning principal $\mathbf G$-bundles
Sbornik. Mathematics, Tome 211 (2020) no. 12, pp. 1777-1794

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The main results of the paper are two purity theorems for reductive group schemes over regular local rings containing a field. Using these two theorems a well-known Grothendieck-Serre conjecture on principal bundles is reduced to the simply-connected case. We point out that the mentioned reduction is one of the major steps in the proof of the conjecture that the author published in another work. Bibliography: 25 titles.
Keywords: reductive group schemes, principal bundles, purity theorems, Grothendieck-Serre conjecture. 
@article{SM_2020_211_12_a3,
     author = {I. A. Panin},
     title = {Two purity theorems and the {Grothendieck-Serre} conjecture concerning principal $\mathbf G$-bundles},
     journal = {Sbornik. Mathematics},
     pages = {1777--1794},
     publisher = {mathdoc},
     volume = {211},
     number = {12},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2020_211_12_a3/}
}
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I. A. Panin. Two purity theorems and the Grothendieck-Serre conjecture concerning principal $\mathbf G$-bundles. Sbornik. Mathematics, Tome 211 (2020) no. 12, pp. 1777-1794. http://geodesic.mathdoc.fr/item/SM_2020_211_12_a3/