An upper bound on the number of rational points of arbitrary projective varieties over finite fields
Algebraic Geometry
2015-11-03 v3 Combinatorics
Number Theory
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.
Keywords
Cite
@article{arxiv.1409.7544,
title = {An upper bound on the number of rational points of arbitrary projective varieties over finite fields},
author = {Alain Couvreur},
journal= {arXiv preprint arXiv:1409.7544},
year = {2015}
}