Complete reducibility and separable field extensions

Details Complete reducibility and separable field extensions Complete reducibility and separable field extensions

2010-02-23

arxiv.org/abs/1002.4319v3

Mathematics

Group Theory

5 pages; to appear in Comptes rendus Mathematique

Scientific paper

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.

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