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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On a theorem of Ax


Author: Shulim Kaliman
Journal: Proc. Amer. Math. Soc. 133 (2005), 975-977
MSC (2000): Primary 14E25, 14R10
Published electronically: August 4, 2004
MathSciNet review: 2117196
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Abstract: We show that in the case of affine and complete algebraic varieties over an algebraically closed field of zero characteristics any endomorphism of such a variety, that is injective on the complement to a subvariety of codimension $2$, is an automorphism.


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Additional Information

Shulim Kaliman
Affiliation: Department of Mathematics, University of Miami, Coral Gables, Florida 33124
Email: kaliman@math.miami.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07651-8
PII: S 0002-9939(04)07651-8
Received by editor(s): June 5, 2002
Received by editor(s) in revised form: November 20, 2003
Published electronically: August 4, 2004
Additional Notes: The author was partially supported by NSA grant MDA904-03-1-0009
Communicated by: Michael Stillman
Article copyright: © Copyright 2004 American Mathematical Society