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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Spécialisation de la $R$-équivalence pour les groupes réductifs


Author: Philippe Gille
Translated by:
Journal: Trans. Amer. Math. Soc. 356 (2004), 4465-4474
MSC (2000): Primary 20G15, 14L40
Published electronically: January 13, 2004
MathSciNet review: 2067129
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Abstract: Soit $G/k$ un groupe réductif défini sur un corps $k$ de caractéristique distincte de $2$. On montre que le groupes des classes de $R$-équivalence de $G(k)$ne change pas lorsque l'on passe de $k$ au corps des séries de Laurent $k((t))$, c'est-à-dire que l'on a un isomorphisme naturel $G(k)/R \buildrel\sim\over\longrightarrow G\bigl( k((t)) \bigr)/R$.


ABSTRACT. Let $G/k$ be a reductive group defined over a field of characteristic $\not =2$. We show that the group of $R$-equivalence for $G(k)$ is invariant by the change of fields $k((t))/k$ given by the Laurent series. In other words, there is a natural isomorphism $G(k)/R \buildrel\sim\over\longrightarrow G\bigl( k((t)) \bigr)/R$.


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Additional Information

Philippe Gille
Affiliation: UMR 8628 du C.N.R.S., Mathématiques, Bâtiment 425, Université de Paris-Sud, F-91405 Orsay, France
Email: gille@math.u-psud.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03443-9
PII: S 0002-9947(04)03443-9
Received by editor(s): April 9, 2003
Received by editor(s) in revised form: May 9, 2003
Published electronically: January 13, 2004
Article copyright: © Copyright 2004 American Mathematical Society