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- Title
On abelian covers of the projective line with fixed gonality and many rational points.
- Authors
Faber, Xander; Vermeulen, Floris
- Abstract
A smooth geometrically connected curve over the finite field q with gonality γ has at most γ (q + 1) rational points. Faber and Grantham conjectured that there exist curves of every sufficiently large genus with gonality γ that achieve this bound. In this paper, we show that this bound can be achieved for an infinite sequence of genera using abelian covers of the projective line. We also argue that abelian covers will not suffice to prove the full conjecture.
- Subjects
ELLIPTIC curves; LOGICAL prediction
- Publication
International Journal of Number Theory, 2022, Vol 18, Issue 10, p2211
- ISSN
1793-0421
- Publication type
Article
- DOI
10.1142/S1793042122501123