Very special algebraic groups

2020/02/17 by Brion, Michel, Peyre, Emmanuel
#14L10 (Primary) 14M17 #20G15 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2002.06940

Abstract

We say that a smooth algebraic group G over a field k is very special if for any field extension K/k, every G_K-homogeneous K-variety has a K-rational point. It is known that every split solvable linear algebraic group is very special. In this note, we show that the converse holds, and discuss its relationship with the birational classification of algebraic group actions.

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