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arXiv:1108.4975 [math.AG]AbstractReferencesReviewsResources

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

Masaaki Homma

Published 2011-08-25Version 1

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

Comments: 9 pages, presented at the Fq10 conference
Categories: math.AG
Subjects: 14G15, 11G20, 14H25
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