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arXiv · 2605.09166

Rational points on smooth surfaces in $\mathbb{P}^3$ over finite fields

Yves Aubry·José Felipe Voloch
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Abstract

We improve a bound due to the second author on number of rational points on smooth surfaces in $\mathbb{P}^3$ over finite fields and look at families of surfaces that achieve or nearly achieve this bound, for which we compute their exact number of rational points. These computations may have independent interest.

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Yves Aubry, José Felipe Voloch. 2026-05-09. Rational points on smooth surfaces in $\mathbb{P}^3$ over finite fields. https://arxiv.org/abs/2605.09166

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