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

If G is a connected, solvable, algebraic group acting regularly on a non-empty, complete algebraic variety V over an algebraically closed field k, then there is a G fixed-point of V.

References

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

External links

• V.P. Platonov (2001), "Borel fixed-point theorem", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4