The University of Sydney
School of Mathematics and Statistics  
Algebra Seminar  
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University of Sydney Algebra Seminar

Adam Parusinski (Université d'Angers)

Wednesday 4th May, 4-5pm, 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.