English

Complete reducibility and separable field extensions

Group Theory 2010-04-15 v3 Representation Theory

Abstract

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.

Keywords

Cite

@article{arxiv.1002.4319,
  title  = {Complete reducibility and separable field extensions},
  author = {Michael Bate and Benjamin Martin and Gerhard Roehrle},
  journal= {arXiv preprint arXiv:1002.4319},
  year   = {2010}
}

Comments

5 pages; to appear in Comptes rendus Mathematique

R2 v1 2026-06-21T14:50:12.135Z