IJPAM: Volume 78, No. 7 (2012)

GALOIS GROUPS OF FUNCTION FIELDS
WITH INFINITELY MANY AUTOMORPHISMS

C. Alvarez-Garcia$^1$, G. Villa-Salvador$^2$
$^1$Universidad Autónoma Metropolitana-I
Departamento de Matemáticas
09340, México D.F., México
$^2$CINVESTAV IPN
Departamento de Control Automático
Apartado postal 14-740
07000, México, D.F., México


Abstract. Let $E/k(x)$ be a separable geometric extension such that the pole divisor of $x$ is ramified. Let $K/k$ be a function field of genus at least one such that $\Aut_kK$ is infinite. If $K/k$ is elliptic we suppose that the characteristic is zero. The main result of the paper is that there are infinitely many non-isomorphic function fields $L$ over $k$ such that $L/K$ is a Galois extension and $\Gal(L/K)=\Aut_kL\cong\Aut_{k(x)}E$.

Received: February 15, 2012

AMS Subject Classification: 11R58, 11R32, 12F12, 14H52

Key Words and Phrases: inverse Galois problem, geometric extension, infinite automorphism group, moduli field, $C$-improvement

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 78
Issue: 7