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


The cancellation problem for function fields

Author: James K. Deveney
Journal: Proc. Amer. Math. Soc. 103 (1988), 363-364
MSC: Primary 12F20
MathSciNet review: 943046
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Abstract: Let $ L$ be a finitely generated extension of $ K$. We call $ L$ rigid over $ K$ if the set of $ K$-endomorphisms of $ L$ is finite. If $ L$ is rigid over $ K$ and $ x$ is transcendental over $ L$, then $ L$ is invariant under automorphisms of $ L\left( x \right)$ over $ K$ (Theorem 2). This result is used to show that the cancellation property holds for function fields of varieties of general type in characteristic 0.

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PII: S 0002-9939(1988)0943046-1
Article copyright: © Copyright 1988 American Mathematical Society