SINGULAR CURVES AND THE ETALE BRAUER-MANIN OBSTRUCTION FOR SURFACES

被引：0

作者：

Harpaz, Yonatan ^{[1
]}

Skorobogatov, Alexei N. ^{[2
,3
]}

机构：

[1] Radboud Univ Nijmegen, Inst Math Astrophys & Particle Phys, NL-6525 AJ Nijmegen, Netherlands

[2] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2BZ, England

[3] Russian Acad Sci, Inst Informat Transmiss Problems, Moscow 127994, Russia

来源：

ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE | 2014年 / 47卷 / 04期

关键词：

RATIONAL-POINTS; DESCENT;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give an elementary construction of a smooth and projective surface over an arbitrary number field k that is a counterexample to the Hasse principle but has infinite etale Brauer-Manin set. Our surface has a surjective morphism to a curve with exactly one k-point such that the unique k-fibre is geometrically a union of projective lines with an adelic point and the trivial Brauer group, but no k-point.

引用

页码：765 / 778

页数：14