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The Cancellation Problem for Function Fields

James K. Deveney
Proceedings of the American Mathematical Society
Vol. 103, No. 2 (Jun., 1988), pp. 363-364
DOI: 10.2307/2047141
Stable URL: http://www.jstor.org/stable/2047141
Page Count: 2
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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 $L(x)$ 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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