The cancellation problem for function fields

Deveney, James K.

doi:10.1090/S0002-9939-1988-0943046-1

The cancellation problem for function fields
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by James K. Deveney PDF

Proc. Amer. Math. Soc. 103 (1988), 363-364 Request permission

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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