Borel fixed-point theorem

The result was proved by Armand Borel (1956).

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. A more general version of the theorem holds over a field k that is not necessarily algebraically closed.

A solvable algebraic group G is split over k or k-split if G admits a composition series whose composition factors are isomorphic (over k) to the additive 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]

This algebraic geometry–related article is a stub.