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Injective endomorphisms
of varieties and schemes
James Burton Ax |
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Vol. 31 (1969), No. 1, 1–7
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Abstract |
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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
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Milestones
Received: 6 December 1968
Published: 1 October 1969
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Authors |
| James Burton Ax | |
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