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

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