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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 automorphism group of a function field

Authors: Manohar Madan and Michael Rosen
Journal: Proc. Amer. Math. Soc. 115 (1992), 923-929
MSC: Primary 12F12; Secondary 11R58
MathSciNet review: 1088443
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Abstract: Let $ k$ be an algebraically closed field, $ K$ a function field in one variable over $ k$ , and $ G$ a nontrivial finite group. It is proven that there exist infinitely many Galois extensions $ L/K$ such that $ \operatorname{Gal} (L/K)$ is isomorphic to $ G$ , and $ \operatorname{Gal} (L/K) = {\operatorname{Aut} _k}(L)$. This extends to arbitrary characteristic, a result first proven in the case $ k = \mathbb{C}$ by Greenberg in 1974.

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PII: S 0002-9939(1992)1088443-2
Article copyright: © Copyright 1992 American Mathematical Society