Differential operators and hyperelliptic curves over finite fields

Iván Blanco-Chacón, Alberto F. Boix, Stiofáin Fordham, Emrah Sercan Yilmaz

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Boix, De Stefani and Vanzo have characterised ordinary/supersingular elliptic curves over Fp in terms of the level of the defining cubic homogeneous polynomial. We extend their study to arbitrary genus, in particular we prove that every ordinary hyperelliptic curve C of genus g≥2 has level 2. We provide a good number of examples and raise a conjecture.

Original languageEnglish
Pages (from-to)351-370
Number of pages20
JournalFinite Fields and Their Applications
Volume51
DOIs
StatePublished - 1 May 2018

Keywords

  • Algorithm
  • Differential operator
  • Frobenius map
  • Prime characteristic

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Algebra and Number Theory
  • Engineering (all)
  • Applied Mathematics

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