Vol. 31, No. 1, 1969

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Injective endomorphisms of varieties and schemes

James Burton Ax

Vol. 31 (1969), No. 1, 1–7
Abstract

It is shown that every injective endomorphism of a scheme Y of finite type over a scheme X is surjective. The proof is easily reduced to the case where X is field which in turn follows from the analogous result for algebraic varieties. This result is proved using model theoretic methods to transfer the corresponding and trivially true fact about finite fields.

Mathematical Subject Classification
Primary: 14.15
Milestones
Received: 6 December 1968
Published: 1 October 1969
Authors
James Burton Ax