Borel fixed-point theorem

In mathematics, the Borel fixed-point theorem is a fixed-point theorem in algebraic geometry generalizing the Lie-Kolchin theorem. The result was proved by Armand Borel (1956).

Statement of the theorem

Let G be a connected, solvable algebraic group acting regularly on a non-empty, complete algebraic variety V over an algebraically closed field k. Then G has a fixed point in V.

References

• Borel, Armand (1956). "Groupes linéaires algébriques". Ann. Math. (2). 64 (1). Annals of Mathematics: 20–82. doi:10.2307/1969949. JSTOR 1969949. MR 0093006.

External links

• V.P. Platonov (2001) [1994], "Borel fixed-point theorem", Encyclopedia of Mathematics, EMS Press