Borel's fixed point theorem

《Naive Lie Theory》 · 印刷第 21 页 Chapter 2 章首域的约定、第 102 页 Section 6.2，Theorem 6.2.6 完整陈述（省略中间内容）

$k$ is an algebraically closed field and $F$ a subfield. All algebraic varieties are over $k$. […] (Borel's fixed point theorem) Let $G$ be a connected solvable linear algebraic group and $X$ a complete $G$-variety. There exists a point in $X$ that is fixed by all elements of $G$.