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Comptes Rendus Mathématique
Volume 348, n° 9-10
pages 495-497 (mai 2010)
Doi : 10.1016/j.crma.2010.04.013
Received : 27 February 2010 ;  accepted : 6 April 2010
Complete reducibility and separable field extensions
Complète réductibilité et extensions de corps séparables

Michael Bate a , Benjamin Martin b , Gerhard Röhrle c
a Department of Mathematics, University of York, York YO10 5DD, United Kingdom 
b Mathematics and Statistics Department, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand 
c Fakultät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany 


Let G be a connected reductive linear algebraic group. The aim of this note is to settle a question of J-P. Serre concerning the behaviour of his notion of G -complete reducibility under separable field extensions. Part of our proof relies on the recently established Tits Centre Conjecture for the spherical building of the reductive group G .

The full text of this article is available in PDF format.

Soit G un groupe algébrique linéaire réductif connexe. Le but de cette Note est de répondre à une question de J-P. Serre concernant le comportement par extensions de corps séparables, de la notion de G -réductibilité complète qu’il a introduite. Une partie de nos arguments repose sur la solution récente de la conjecture du centre de Tits pour les immeubles sphériques du groupe réductif G .

The full text of this article is available in PDF format.

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