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arXiv · 2002.06940

Very special algebraic groups

Michel Brion·Emmanuel Peyre
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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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Michel Brion, Emmanuel Peyre. 2020-02-17. Very special algebraic groups. https://arxiv.org/abs/2002.06940

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