IJPAM: Volume 78, No. 7 (2012)
GALOIS GROUPS OF FUNCTION FIELDS
WITH INFINITELY MANY AUTOMORPHISMS
WITH INFINITELY MANY AUTOMORPHISMS
C. Alvarez-Garcia
, G. Villa-Salvador
Universidad Autónoma Metropolitana-I
Departamento de Matemáticas
09340, México D.F., México
CINVESTAV IPN
Departamento de Control Automático
Apartado postal 14-740
07000, México, D.F., México



Departamento de Matemáticas
09340, México D.F., México

Departamento de Control Automático
Apartado postal 14-740
07000, México, D.F., México
Abstract. Let be a separable geometric
extension such
that the pole divisor of
is ramified. Let
be a function field of genus at least one such that
is
infinite. If
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
over
such that
is a Galois extension and
.
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, -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