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
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