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Izvestiya: Mathematics, 2016, Volume 80, Issue 4, Pages 759–790
DOI: https://doi.org/10.1070/IM8452 (Mi im8452) 		 
This article is cited in 5 scientific papers (total in 5 papers)

On Grothendieck–Serre's conjecture concerning principal $G$-bundles over reductive group schemes: II

I. A. Panin

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
English version PDF (476 kB) Citations (5)
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DOI: https://doi.org/10.1070/IM8452
Abstract: A proof of the Grothendieck–Serre conjecture on principal bundles over a semi-local regular ring containing an infinite field is given in [1]. That proof is heavily based on Theorem 1.0.3 stated below in the introduction and proved in the present paper.
Theorem 1.0.3 itself is a consequence of two purity theorems 1.0.1 and 1.0.2 which are of completely independent interest and which are proved below. The purity theorem 1.0.1 covers all the known results of this shape and looks like a final one.
Keywords: reductive group schemes, principal bundles, Grothendieck–Serre conjecture.
Funding agency Grant number
Russian Science Foundation 14-11-00456
The author acknowledges the support of the Russian Science Foundation (grant no. 14-11-00456).
Received: 08.10.2015
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2016, Volume 80, Issue 4, Pages 131–162
DOI: https://doi.org/10.4213/im8452
Bibliographic databases:
Document Type: Article
UDC: 512.74+512.723
MSC: 20G35, 14L15, 20G41, 20G99
Language: English
Original paper language: English
Citation: I. A. Panin, “On Grothendieck–Serre's conjecture concerning principal $G$-bundles over reductive group schemes: II”, Izv. RAN. Ser. Mat., 80:4 (2016), 131–162; Izv. Math., 80:4 (2016), 759–790
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    References:56
    First page:26
     
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