Geodesic
A proof of the Grothendieck–Serre conjecture on principal bundles over regular local rings containing infinite fields
Fedorov, Roman1 ; Panin, Ivan2 
1 Mathematics Department, Kansas State University 138 Cardwell Hall 66506 Manhattan KS USA
2 Steklov Institute of Mathematics at St.-Petersburg Fontanka 27 191023 St.-Petersburg Russia
Publications Mathématiques de l'IHÉS, Tome 122 (2015), pp. 169-193

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Let R be a regular local ring containing an infinite field. Let G be a reductive group scheme over R. We prove that a principal G-bundle over R is trivial if it is trivial over the fraction field of R. In other words, if K is the fraction field of R, then the map of non-abelian cohomology pointed sets

He´t1(R,G)→He´t1(K,G)
induced by the inclusion of R into K has a trivial kernel.

DOI : 10.1007/s10240-015-0075-z
Keywords: Algebraic Group, Group Scheme, Principal Bundle, Monic Polynomial, Closed Subscheme

Fedorov, Roman 1 ; Panin, Ivan 2

1 Mathematics Department, Kansas State University 138 Cardwell Hall 66506 Manhattan KS USA
2 Steklov Institute of Mathematics at St.-Petersburg Fontanka 27 191023 St.-Petersburg Russia 
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     title = {A proof of the {Grothendieck{\textendash}Serre} conjecture on principal bundles over regular local rings containing infinite fields},
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Fedorov, Roman; Panin, Ivan. A proof of the Grothendieck–Serre conjecture on principal bundles over regular local rings containing infinite fields. Publications Mathématiques de l'IHÉS, Tome 122 (2015), pp. 169-193. doi: 10.1007/s10240-015-0075-z

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