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. Of Math. (2) (Annals of Mathematics) 64 (1): 20–82. doi:10.2307/1969949. JSTOR 1969949. MR0093006. 

External links

• V.P. Platonov (2001), "Borel fixed-point theorem", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1556080104, http://www.encyclopediaofmath.org/index.php?title=b/b017070