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.
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页码：765 / 778
页数：14
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