A bound on the number of points of a curve in projective space over a finite field

Abstract

For a nondegenerate irreducible curve $C$ of degree $d$ in ${\mathbb{P}}^r$ over ${\mathbb{F}}_q$ with $r\ge 3$, we prove that the number $N_q(C)$ of ${\mathbb{F}}_q$-points of $C$ satisfies the inequality $N_q(C)\le (d-1)q+1$, which is known as Sziklai's bound if $r=2$.

arXiv comment9 pages, presented at the Fq10 conference

Cited by in corpus (1)

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