NDLI: The Automorphism Group of a Function Field

Content Provider	Scilit
Author	Madan, Manohar Rosen, Michael
Copyright Year	1992
Description	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.
Related Links	https://www.ams.org/proc/1992-115-04/S0002-9939-1992-1088443-2/S0002-9939-1992-1088443-2.pdf
Ending Page	929
Page Count	7
Starting Page	923
ISSN	00029939
e-ISSN	10886826
DOI	10.2307/2159335
Journal	Proceedings of the American Mathematical Society
Issue Number	4
Volume Number	115
Language	English
Publisher	Duke University Press
Publisher Date	1992-08-01
Access Restriction	Open
Subject Keyword	Logic Automorphism Group Function Field Greenberg Infinitely Nontrivial Isomorphic
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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The Automorphism Group of a Function Field