Complete reducibility and separable field extensions
classification
🧮 math.GR
math.RT
keywords
extensionsfieldgroupreducibilityreductiveseparablealgebraicbehaviour
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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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