A note on Nullstellensatz over finite fields

被引：12

作者：

Ghorpade, Sudhir R. ^{[1
]}

机构：

[1] Indian Inst Technol, Dept Math, Mumbai 400076, Maharashtra, India

来源：

CONTRIBUTIONS IN ALGEBRA AND ALGEBRAIC GEOMETRY | 2019年 / 738卷

关键词：

Nullstellensatz; finite field; vanishing ideal; affine space; projective space; footprint; REED-MULLER CODES; PROOF;

D O I：

10.1090/conm/738/14876

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give an expository account of Nullstellensatz-like results when the base field is finite. In particular, we discuss the vanishing ideal of the affine space and of the projective space over a finite field. As an application, we include an alternative proof of Ore's inequality for the number of points of affine hypersurfaces over finite fields.

引用

页码：23 / 32

页数：10

共 24 条

[1] Another elementary proof of the Nullstellensatz [J].

Arrondo, E .

AMERICAN MATHEMATICAL MONTHLY, 2006, 113 (02) :169-171

[2] QUADRATIC TORSION AND SELF-DUAL NORMAL BASES [J].

BAYERFLUCKIGER, E ;

SERRE, JP .

AMERICAN JOURNAL OF MATHEMATICS, 1994, 116 (01) :1-64

[3] Vanishing Ideals of Projective Spaces over Finite Fields and a Projective Footprint Bound [J].

Beelen, Peter ;

Datta, Mrinmoy ;

Ghorpade, Sudhir R. .

ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2019, 35 (01) :47-63

[4]

Carvalho C., 2017, LECT NOTES CIMPA RES

[5]

Cox D., 1992, UNDERGRADUATE TEXTS

[6] ON A CONJECTURE OF TSFASMAN AND AN INEQUALITY OF SERRE FOR THE NUMBER OF POINTS OF HYPERSURFACES OVER FINITE FIELDS [J].

Datta, Mrinmoy ;

Ghorpade, Sudhir R. .

MOSCOW MATHEMATICAL JOURNAL, 2015, 15 (04) :715-725

[7] ON GENERALIZED REED-MULLER CODES AND THEIR RELATIVES [J].

DELSARTE, P ;

GOETHALS, JM ;

MACWILLI.FJ .

INFORMATION AND CONTROL, 1970, 16 (05) :403-&

[8]

Eisenbud D., 1995, GRADUATE TEXTS MATH, V150, DOI 10.1007/978-1-4612-5350-1

[9]

Goel K., 2018, ARXIV180902818MATHAC

[10]

Hilbert D., 1893, Mathematische Annalen, V42, P313, DOI 10.1007/BF01444162

← 1 2 3 →