Twists of genus three curves over finite fields

Stephen Meagher, Jakob Top

Research output: Contribution to journalArticleAcademicpeer-review

14 Citations (Scopus)

Abstract

In this article we recall how to describe the twists of a curve over a finite field and we show how to compute the number of rational points on such a twist by methods of linear algebra We illustrate this in the case of plane quartic curves with at least 16 automorphisms In particular we treat the twists of the Dyck-Fermat and Klein quartics. Our methods show how in special cases non-Abelian cohomology can be explicitly computed They also show how questions which appear difficult from a function field perspective can be resolved by using the theory of the Jacobian variety (C) 2010 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)347-368
Number of pages22
JournalFinite fields and their applications
Volume16
Issue number5
DOIs
Publication statusPublished - Sep-2010

Keywords

  • Non-Abelian Galois cohomology
  • Dyck–Fermat quartic
  • Klein quartic
  • Twist
  • Jacobian
  • Curve

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