Existence of rational points on smooth projective varieties

被引：0

作者：

Poonen, Bjorn ^{[1
]}

机构：

[1] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

来源：

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2009年 / 11卷 / 03期

关键词：

Brauer-Manin obstruction; Hasse principle; Chatelet surface; conic bundle; rational points; HILBERTS 10TH PROBLEM; CHATELET SURFACES; FUNCTION-FIELDS; QUADRICS; CHARACTERISTIC-2; INTERSECTIONS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Fix a number field k. We prove that if there is an algorithm for deciding whether a smooth projective geometrically integral k-variety has a k-point, then there is an algorithm for deciding whether an arbitrary k-variety has a k-point and also an algorithm for computing X(k) for any k-variety X for which X(k) is finite. The proof involves the construction of a one-parameter algebraic family of Chatelet surfaces such that exactly one of the surfaces fails to have a k-point.

引用

页码：529 / 543

页数：15

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