The complete list of genera of quotients of the Fq2-maximal Hermitian curve for q≡1 (mod 4)

Maria Montanucci, Giovanni Zini

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Abstract

Let Fq2 be the finite field with q2 elements. Most of the known Fq2 -maximal curves arise as quotient curves of the Fq2 -maximal Hermitian curve Hq. After a seminal paper by Garcia, Stichtenoth and Xing, many papers have provided genera of quotients of Hq, but their complete determination is a challenging open problem. In this paper we determine completely the spectrum of genera of quotients of Hq for any q ≡ 1 (mod 4).
Original languageEnglish
JournalJournal of Algebra
Volume550
Pages (from-to)23-53
ISSN0021-8693
DOIs
Publication statusPublished - 2020

Keywords

  • Hermitian curve
  • Unitary groups
  • Quotient curves
  • Maximal curves

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