The inverse sieve problem for algebraic varieties over global fields

被引：1

作者：

Manuel Menconi, Juan ^{[1
,2
]}

Paredes, Marcelo ^{[2
]}

Sasyk, Roman ^{[1
,2
]}

机构：

[1] Consejo Nacl Invest Cient & Tecn, Inst Argentino Matemat Alberto P Calderon, Saavedra 15,Piso 3, RA-1083 Buenos Aires, DF, Argentina

[2] Univ Buenos Aires, Fac Ciencias Exactas & Nat, Dept Matemat, RA-1428 Buenos Aires, DF, Argentina

来源：

REVISTA MATEMATICA IBEROAMERICANA | 2021年 / 37卷 / 06期

关键词：

Inverse problems; larger sieve over global fields; heights in global fields; varieties over global fields; effective Noether's normalization over global fields; POINTS; HEIGHT;

D O I：

10.4171/rmi/1261

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let K be a global field and let Z be a geometrically irreducible algebraic variety defined over K. We show that if a big set S subset of Z of rational points of bounded height occupies few residue classes modulo p for many prime ideals p, then a positive proportion of S must lie in the zero set of a polynomial of low degree that does not vanish at Z. This generalizes a result of Walsh who studied the case when S subset of {0, ..., N}(d).

引用

页码：2245 / 2284

页数：40

共 50 条

[41] On some local-global principles for linear algebraic groups over infinite algebraic extensions of global fields
Ngo Thi Ngoan
Nguyen Quoc Thang
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2019, 568 : 39 - 83
[42] THE LARGE SIEVE PROCEDURE IN ALGEBRAIC NUMBER-FIELDS
HINZ, JG
[J]. MANUSCRIPTA MATHEMATICA, 1987, 57 (02) : 181 - 194
[43] Tractability of algebraic function fields in one variable of genus one over global fields
Han, Ilseop
[J]. JOURNAL OF ALGEBRA, 2007, 317 (02) : 796 - 812
[44] Tractability of algebraic function fields in one variable of genus zero over global fields
Han, I
[J]. JOURNAL OF ALGEBRA, 2001, 244 (01) : 217 - 235
[45] On the Algorithmic Undecidability of the Embeddability Problem for Algebraic Varieties over a Field of Characteristic Zero
A. Ya. Kanel’-Belov
A. A. Chilikov
[J]. Mathematical Notes, 2019, 106 : 299 - 302
[46] On the Algorithmic Undecidability of the Embeddability Problem for Algebraic Varieties over a Field of Characteristic Zero
Kanel'-Belov, A. Ya.
Chilikov, A. A.
[J]. MATHEMATICAL NOTES, 2019, 106 (1-2) : 299 - 302
[47] ON TORSION OF ABELIAN-VARIETIES OVER LARGE ALGEBRAIC EXTENSIONS OF FINITELY GENERATED FIELDS
JACOBSON, M
JARDEN, M
[J]. MATHEMATIKA, 1984, 31 (61) : 110 - 116
[48] App ell-Lauricella hypergeometric functions over finite fields and algebraic varieties
Nakagawa, Akio
[J]. HOKKAIDO MATHEMATICAL JOURNAL, 2024, 53 (02) : 307 - 347
[49] Uniform bounds for the number of rational points on varieties over global fields
Paredes, Marcelo
Sasyk, Roman
[J]. ALGEBRA & NUMBER THEORY, 2022, 16 (08) : 1941 - 2000
[50] HASSE PRINCIPLE FOR THREE CLASSES OF VARIETIES OVER GLOBAL FUNCTION FIELDS
Tian, Zhiyu
[J]. DUKE MATHEMATICAL JOURNAL, 2017, 166 (17) : 3349 - 3424

← 1 2 3 4 5 →