Classification of all Galois subcovers of the Skabelund maximal curves

被引：2

作者：

Beelen, Peter ^{[1
]}

Landi, Leonardo ^{[1
]}

Montanucci, Maria ^{[1
]}

机构：

[1] Tech Univ Denmark, Dept Appl Math & Comp Sci, Matematiklovet 303B,2800 Kgs, DK-2800 Lyngby, Denmark

来源：

JOURNAL OF NUMBER THEORY | 2023年 / 242卷

关键词：

Suzuki and Ree curves; Skabelund maximal curves; Genus spectrum of maximal curves; DELIGNE-LUSZTIG CURVE; FINITE-FIELDS; ALGEBRAIC-CURVES; QUOTIENT CURVES; SUBFIELDS; SUZUKI; GENERA; GENUS; SPECTRUM; NUMBER;

D O I：

10.1016/j.jnt.2022.07.008

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In 2017 Skabelund constructed two new examples of maximal curves S similar to q and similar to Rq as covers of the Suzuki and Ree curves, respectively. The resulting Skabelund curves are analogous to the Giulietti-Korchmaros cover of the Hermitian curve. In this paper a complete characterization of all Galois subcovers of the Skabelund curves S similar to q and similar to Rq is given. Calculating the genera of the corresponding curves, we find new additions to the list of known genera of maximal curves over finite fields. (c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

引用

页码：46 / 72

页数：27

共 46 条

[1] On the genera of subfields of the Hermitian function field [J].