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Article Dans Une Revue Proceedings of the American Mathematical Society Année : 2016

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

Résumé

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.

Dates et versions

hal-01069510 , version 1 (29-09-2014)

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Alain Couvreur. An upper bound on the number of rational points of arbitrary projective varieties over finite fields. Proceedings of the American Mathematical Society, 2016, 144 (9), pp.3671-3685. ⟨10.1090/proc/13015⟩. ⟨hal-01069510⟩
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