Twists of genus three curves over finite fields

Stephen Meagher, Jakob Top

OnderzoeksoutputAcademicpeer review

15 Citaten (Scopus)


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.

Originele taal-2English
Pagina's (van-tot)347-368
Aantal pagina's22
TijdschriftFinite fields and their applications
Nummer van het tijdschrift5
StatusPublished - sep-2010

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