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01164nam a2200193Ia 4500 |
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10.1142-S1793042122501123 |
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220630s2022 CNT 000 0 und d |
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|a 17930421 (ISSN)
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|a On abelian covers of the projective line with fixed gonality and many rational points
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|b World Scientific
|c 2022
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|a 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. © 2022 World Scientific Publishing Company.
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|a class field theory
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|a Curves over finite fields
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|a gonality
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|a rational points
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|a Faber, X.
|e author
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|a Vermeulen, F.
|e author
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| 773 |
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|t International Journal of Number Theory
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| 856 |
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|z View Fulltext in Publisher
|u https://doi.org/10.1142/S1793042122501123
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