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

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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Contributor : Alain Couvreur <>
Submitted on : Monday, September 29, 2014 - 12:50:19 PM
Last modification on : Wednesday, March 27, 2019 - 4:41:27 PM

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  • HAL Id : hal-01069510, version 1
  • ARXIV : 1409.7544

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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, American Mathematical Society, 2016, 144, pp.3671-3685. ⟨http://www.ams.org/journals/proc/2016-144-09/S0002-9939-2016-13015-3/⟩. ⟨hal-01069510⟩

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