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Zapiski Nauchnykh Seminarov POMI, 2016, Volume 443, Pages 133–146 (Mi znsl6262)  
This article is cited in 8 scientific papers (total in 8 papers)

On the Grothendieck–Serre conjecture concerning principal $G$-bundles over semi-local Dedekind domains

I. A. Panina, A. K. Stavrovab

a Steklov Institute of Mathematics at St. Petersburg, Fontanka 27, St. Petersburg 191023, Russia
b Department of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia
Full-text PDF (234 kB) Citations (8)
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Abstract: 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].
Key words and phrases: reductive group, principal bundle.
Funding agency Grant number
Russian Science Foundation 14-11-00456
Saint Petersburg State University 6.50.22.2014
Theorem 3.4 is proved due to the support of the Russian Science Foundation (grant no. 14-11-00456).
The second author is a postdoctoral fellow of the program 6.50.22.2014 “Structure theory, representation theory and geometry of algebraic groups” at St. Petersburg State University.
Received: 02.12.2015
English version:
Journal of Mathematical Sciences (New York), 2017, Volume 222, Issue 4, Pages 453–462
DOI: https://doi.org/10.1007/s10958-017-3316-5
Bibliographic databases:
Document Type: Article
UDC: 512
Language: English
Citation: I. A. Panin, A. K. Stavrova, “On the Grothendieck–Serre conjecture concerning principal $G$-bundles over semi-local Dedekind domains”, Problems in the theory of representations of algebras and groups. Part 29, Zap. Nauchn. Sem. POMI, 443, POMI, St. Petersburg, 2016, 133–146; J. Math. Sci. (N. Y.), 222:4 (2017), 453–462
Citation in format AMSBIB
\Bibitem{PanSta16}
\by I.~A.~Panin, A.~K.~Stavrova
\paper On the Grothendieck--Serre conjecture concerning principal $G$-bundles over semi-local Dedekind domains
\inbook Problems in the theory of representations of algebras and groups. Part~29
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 443
\pages 133--146
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6262}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3507770}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 222
\issue 4
\pages 453--462
\crossref{https://doi.org/10.1007/s10958-017-3316-5}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85014763197}
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    • This publication is cited in the following 8 articles:
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