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 Zap. Nauchn. Sem. POMI, 2020, Volume 490, Pages 98–103 (Mi znsl6930)

A purity theorem for quadratic spaces

I. Panin

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences

Abstract: It is proved a purity theorem for quadratic spaces over semi-local regular integral domain containing a field of odd characteristic. This theorem extends to the semi-local case the corresponding results proven previously by the author and by the author jointly with K. Pimenov. To get this result we extend the purity theorem of Ojanguren–Panin to this more general setting.

Key words and phrases: quadratic form, regular local ring, isotropic vector, Grothendieck–Serre conjecture.

 Funding Agency Grant Number Russian Foundation for Basic Research 19-01-00513 The author acknowledges support of the RFBR grant No. 19-01-00513.

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Citation: I. Panin, “A purity theorem for quadratic spaces”, Algebra and number theory. Part 3, Zap. Nauchn. Sem. POMI, 490, POMI, St. Petersburg, 2020, 98–103

Citation in format AMSBIB
\Bibitem{Pan20} \by I.~Panin \paper A purity theorem for quadratic spaces \inbook Algebra and number theory. Part~3 \serial Zap. Nauchn. Sem. POMI \yr 2020 \vol 490 \pages 98--103 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl6930}