An upper bound on the number of rational points of arbitrary projective varieties over finite fields

Alain Couvreur

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arXiv · 1409.7544

An upper bound on the number of rational points of arbitrary projective varieties over finite fields

Alain Couvreur

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Abstract

We give an upper bound on the number of rational points of an arbitrary Zariski closed subset of a projective space over a finite field. This bound depends only on the dimensions and degrees of the irreducible components and holds for very general varieties, even reducible and non equidimensional. As a consequence, we prove a conjecture of Ghorpade and Lachaud on the maximal number of rational points of an equidimensional projective variety.

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Alain Couvreur. 2014-09-26. An upper bound on the number of rational points of arbitrary projective varieties over finite fields. https://arxiv.org/abs/1409.7544

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