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).
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页码：2245 / 2284
页数：40
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