Adam Parusinski
(Université d'Angers)
Wednesday 4th May, 45pm, Carslaw 275
Injective endomorphisms of real algebraic varieties
The theorem of Ax says that any injective regular selfmapping
of an algebraic variety over an algebraically closed field is
surjective. In this talk we first recall the main argument of Ax, a
reduction to the finite field case. Then we present a different,
topological proof of Ax's theorem for complex algebraic varieties due to
Borel. Finally we extend Borel's idea and show that any injective
regular selfmapping of a real algebraic variety is a homeomorphism.
