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arXiv · 1801.09139

Vanishing ideals of projective spaces over finite fields and a projective footprint bound

Peter Beelen·Mrinmoy Datta·Sudhir R. Ghorpade
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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

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Peter Beelen, Mrinmoy Datta, Sudhir R. Ghorpade. 2018-01-27. Vanishing ideals of projective spaces over finite fields and a projective footprint bound. https://arxiv.org/abs/1801.09139

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