Some families of nonisomorphic maximal function fields
Abstract
The problem of understanding whether two given function fields are isomorphic is wellknown to be difficult, particularly when the aim is to prove that an isomorphism does not exist. In this paper we investigate a family of maximal function fields that arise as Galois subfields of the Hermitian function field. We compute the automorphism group, the Weierstrass semigroup at some special rational places and the isomorphism classes of such function fields. In this way, we show that often these function fields provide in fact examples of maximal function fields with the same genus, the same automorphism group, but that are not isomorphic.
 Publication:

arXiv eprints
 Pub Date:
 April 2024
 DOI:
 10.48550/arXiv.2404.14179
 arXiv:
 arXiv:2404.14179
 Bibcode:
 2024arXiv240414179B
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Algebraic Geometry;
 11G;
 14G