Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 $G(k)/R \buildrel\sim\over\longrightarrow G\bigl( k((t)) \bigr)/R$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 20G15, 14L40

Retrieve articles in all journals with MSC (2000): 20G15, 14L40

Additional Information

Philippe Gille
Affiliation: UMR 8628 du C.N.R.S., Mathématiques, Bâtiment 425, Université de Paris-Sud, F-91405 Orsay, France

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

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia