The number of varieties in a family which contain a rational point

被引：11

作者：

Loughran, Daniel ^{[1
]}

机构：

[1] Univ Manchester, Sch Math, Oxford Rd, Manchester M13 9PL, Lancs, England

来源：

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2018年 / 20卷 / 10期

关键词：

Rational points; families of varieties; Brauer groups; toric varieties; TERNARY QUADRATIC-FORMS; BOUNDED HEIGHT; MANINS CONJECTURE; HASSE PRINCIPLE; BRAUER GROUP; FIBRATIONS; SURFACES; PENCILS;

D O I：

10.4171/JEMS/818

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the problem of counting the number of varieties in a family over a number field which contain a rational point. In particular, for products of Brauer-Severi varieties and closely related counting functions associated to Brauer group elements. Using harmonic analysis on toric varieties, we provide a positive answer to a question of Serre on such counting functions in some cases. We also formulate some conjectures on generalisations of Serre's problem.

引用

页码：2539 / 2588

页数：50