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Automorphism groups of ruled function fields and a problem of Zariski


Author: James K. Deveney
Journal: Proc. Amer. Math. Soc. 90 (1984), 178-180
MSC: Primary 12F20; Secondary 14H05
DOI: https://doi.org/10.1090/S0002-9939-1984-0727227-4
MathSciNet review: 727227
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Abstract: Let $ {K_1}$ and $ {K_2}$ be finitely generated extensions of a field $ K$ and let $ x$ be transcendental over $ {K_1}$ and $ {K_2}$, and assume $ {K_1}(x) = {K_2}(x)$. The main results show that if $ K$ is infinite and the group of automorphisms of $ {K_2}$ over $ K$ is finite, or if $ K$ is finite and the group of automorphisms of $ \bar K{K_2}$ over $ \bar K$ ($ \bar K$ the algebraic closure of $ K$) is finite, then $ {K_1}$ equals $ {K_2}$.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0727227-4
Keywords: Function field, automorphisms
Article copyright: © Copyright 1984 American Mathematical Society

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