Borel fixed-point theorem explained
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 .
Statement
If G is a connected, solvable, linear 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.
or the
multiplicative group
. If
G is a connected,
k-split solvable algebraic group acting regularly on a complete variety
V having a
k-rational point, then there is a
G fixed-point of
V.
[1] References
- Borel. Armand. Groupes linéaires algébriques. Ann. Math. . 2. 1956. 20 - 82. 64. 10.2307/1969949. 1. Annals of Mathematics. 1969949. 0093006.
Notes and References
- Borel (1991), Proposition 15.2
