Vanishing Ideals of Projective Spaces over Finite Fields and a Projective Footprint Bound

被引：0

作者：

Peter BEELEN ^{[1
]}

Mrinmoy DATTA ^{[1
,2
]}

Sudhir R.GHORPADE ^{[3
]}

机构：

[1] Department of Applied Mathematics and Computer Science,Technical University of Denmark

[2] Department of Mathematics and Statistics,UiT-The Arctic University of Norway

[3] Department of Mathematics,Indian Institute of Technology Bombay

来源：

Acta Mathematica Sinica,English Series | 2019年 / 01期

关键词：

Finite field; projective space; algebraic variety; vanishing ideal; Grbner basis; footprint bound; projective hypersurface;

D O I：

暂无

中图分类号：

O186.1 [微分几何];

学科分类号：

0701 ; 070101 ;

摘要：

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 for the so-called footprint bound, and a version of it that is suitable for estimating the number of rational points of projective algebraic varieties over finite fields. An application to Serre’s inequality for the number of points of projective hypersurfaces over finite fields is included.

引用

页码：47 / 63

页数：17

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