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arXiv · 2008.05748

A bound for the number of points of space curves over finite fields

Peter Beelen·Maria Montanucci
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Abstract

For a non-degenerate irreducible curve $C$ of degree $d$ in $\mathbb{P}^3$ over $\mathbb{F}_q$, we prove that the number $N_q(C)$ of $\mathbb{F}_q$-rational points of $C$ satisfies the inequality $N_q(C) \leq (d-2)q+1$. Our result improves the previous bound $N_q(C) \leq (d-1)q+1$ obtained by Homma in 2012 and leads to a natural conjecture generalizing Sziklai's bound for the number of points of plane curves over finite fields.

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Peter Beelen, Maria Montanucci. 2020-08-13. A bound for the number of points of space curves over finite fields. https://arxiv.org/abs/2008.05748

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