Jump to content

Borel fixed-point theorem

From Wikipedia, the free encyclopedia
This is an old revision of this page, as edited by Citation bot 1 (talk | contribs) at 21:37, 3 June 2010 (Citations: [Pu158]Tweaked: url, publisher, issue. You can use this bot yourself! Report bugs here.). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

In mathematics, the Borel fixed-point theorem is a fixed-point theorem in algebraic geometry. The result was proved by the Swiss mathematician Armand Borel in 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). - 64 (1). Annals of Mathematics: 20–82. doi:10.2307/1969949. MR0093006
Retrieved from "https://en.wikipedia.org/w/index.php?title=Borel_fixed-point_theorem&oldid=365906266"