Varieties over finite fields: quantitative theory

被引：1

作者：

Vladut, S. G. ^{[1
,2
]}

Nogin, D. Yu. ^{[2
]}

Tsfasman, M. A. ^{[2
,3
,4
]}

机构：

[1] Aix Marseille Univ, CNRS, Cent Marseille, I2M,UMR 7373, Marseille, France

[2] Russian Acad Sci, Inst Informat Transmiss Problems, Moscow, Russia

[3] CNRS, Lab Math Versailles, UMR 8100, Paris, France

[4] Independent Univ Moscow, Moscow, Russia

来源：

RUSSIAN MATHEMATICAL SURVEYS | 2018年 / 73卷 / 02期

基金：

俄罗斯科学基金会;

关键词：

algebraic varieties over finite fields; zeta functions; points on surfaces; error-correcting codes; arithmetic statistics; explicit formulae in arithmetic; DEL PEZZO SURFACES; ABELIAN-VARIETIES; ZETA-FUNCTIONS; BIELLIPTIC SURFACES; CONIC BUNDLES; GOPPA CODES; K3; SURFACES; POINTS; NUMBER; TOWERS;

D O I：

10.1070/RM9814

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Algebraic varieties over finite fields are considered from the point of view of their invariants such as the number of points of a variety that are defined over the ground field and its extensions. The case of curves has been actively studied over the last thirty-five years, and hundreds of papers have been devoted to the subject. In dimension two or higher, the situation becomes much more difficult and has been little explored. This survey presents the main approaches to the problem and describes a major part of the known results in this direction.

引用

页码：261 / 322

页数：62

共 50 条

[1] On the number of points on abelian and Jacobian varieties over finite fields
Aubry, Yves
Haloui, Safia
Lachaud, Gilles
ACTA ARITHMETICA, 2013, 160 (03) : 201 - 241
[2] Tame class field theory for singular varieties over finite fields
Geisser, Thomas
Schmidt, Alexander
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2017, 19 (11) : 3467 - 3488
[3] Tate conjecture for products of Fermat varieties over finite fields
Sugiyama, Rin
MANUSCRIPTA MATHEMATICA, 2014, 144 (3-4) : 421 - 438
[4] On the order of CM abelian varieties over finite prime fields
Spreckels, Ute
FINITE FIELDS AND THEIR APPLICATIONS, 2017, 45 : 386 - 405
[5] Abelian varieties over fields of finite characteristic
Zarhin, Yuri G.
CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2014, 12 (05): : 659 - 674
[6] Isogenies of abelian varieties over finite fields
Alice Silverberg
Yuri G. Zarhin
Designs, Codes and Cryptography, 2015, 77 : 427 - 439
[7] Isogenies of abelian varieties over finite fields
Silverberg, Alice
Zarhin, Yuri G.
DESIGNS CODES AND CRYPTOGRAPHY, 2015, 77 (2-3) : 427 - 439
[8] Categories of abelian varieties over finite fields, I: Abelian varieties over Fp
Centeleghe, Tommaso Giorgio
Stix, Jakob
ALGEBRA & NUMBER THEORY, 2015, 9 (01) : 225 - 265
[9] Computing base extensions of ordinary abelian varieties over finite fields
Marseglia, Stefano
INTERNATIONAL JOURNAL OF NUMBER THEORY, 2022, 18 (09) : 1957 - 1974
[10] Frobenius Distributions of Low Dimensional Abelian Varieties Over Finite Fields
Arango-Pineros, Santiago
Bhamidipati, Deewang
Sankar, Soumya
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2024, 2024 (16) : 11989 - 12020

← 1 2 3 4 5 →