Vanishing ideals of projective spaces over finite fields and a projective footprint bound
Algebraic Geometry
2018-07-18 v2
Abstract
We consider the vanishing ideal of a projective space over a finite field. An explicit set of generators for this ideal has been given by Mercier and Rolland. We show that these generators form a universal Gr\"obner basis of the ideal. Further we give a projective analogue of the footprint bound, and a version of it that is suitable for estimating the number of points of a projective algebraic variety over a finite field. An application to Serre's inequality for the number of rational points of projective hypersurfaces over finite fields is included
Keywords
Cite
@article{arxiv.1801.09139,
title = {Vanishing ideals of projective spaces over finite fields and a projective footprint bound},
author = {Peter Beelen and Mrinmoy Datta and Sudhir R. Ghorpade},
journal= {arXiv preprint arXiv:1801.09139},
year = {2018}
}
Comments
16 pages, slightly revised version, to appear in Acta Math. Sin. (Engl. Ser.)