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

作     者：Peter BEELEN Mrinmoy DATTA Sudhir R.GHORPADE 

作者机构：Department of Applied Mathematics and Computer ScienceTechnical University of DenmarkDK 2800.Kgs.LyngbyDenmark Department of Applied Mathematics and Computer ScienceTechnical University of DenmarkDK 2800Kgs.LyngbyDenmark Current address:Department of Mathematics and StatisticsUiT-The Arctic Unwersity ofNorwayN-9037TromsφNorway Department of MathematicsIndian Institute of Technology BombayPowaiMumbai 400076India 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2019年第35卷第1期

页      面：47-63页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the Danish Council for Independent Research(Grant No.DFF–4002-00367),supported by the Danish Council for Independent Research(Grant No.DFF–6108-00362) supported by the Research Council of Norway(Project No.280731) supported by IRCC Award grant 12IRAWD009 from IIT Bombay 

主　　题：Finite field projective space algebraic variety vanishing ideal Grbner basis footprint bound projective hypersurface 

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.