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

Fuente: arXiv
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Main Authors: Aubry, Yves, Voloch, José Felipe
Format: Preprint
Published: 2026
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author Aubry, Yves
Voloch, José Felipe
author_facet Aubry, Yves
Voloch, José Felipe
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2605_09166
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Rational points on smooth surfaces in $\mathbb{P}^3$ over finite fields
Aubry, Yves
Voloch, José Felipe
Number Theory
Algebraic Geometry
11G25, 14G15
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.
title Rational points on smooth surfaces in $\mathbb{P}^3$ over finite fields
topic Number Theory
Algebraic Geometry
11G25, 14G15
url https://arxiv.org/abs/2605.09166