Work

Non-isomorphic maximal function fields of genus q − 1

Year: 2025

Type: article

Abstract: The classification of maximal function fields over a finite field is a difficult open problem, and even determining isomorphism classes among known function fields is challenging in general. We study a particular family of maximal function fields defined over a finite field with q 2 elements, where q is the power of an odd prime. When d : = ( q + 1 ) / 2 is a prime, this family is known to contain a large number of non-isomorphic function fields of the same genus and with the same automorphism group. We compute the automorphism group and isomorphism classes also in the case where d is not a prime.

Source: Finite Fields and Their Applications

DOI: 10.1016/j.ffa.2025.102618

Author: Jonathan Niemann

Institution: Technical University of Denmark

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,720

OpenAlex ID: W4408657269

FWCI:

Cites: 13

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Related to: 10