Rational points on pencils of conics and quadrics with many degenerate fibres

被引：23

作者：

Browning, T. D. ^{[1
]}

Matthiesen, L. ^{[2
]}

Skorobogatov, A. N. ^{[3
,4
]}

机构：

[1] Univ Bristol, Bristol, Avon, England

[2] Inst Math Jussieu, Paris, France

[3] Univ London Imperial Coll Sci Technol & Med, London, England

[4] Inst Informat Transmiss Problems, Moscow, Russia

来源：

ANNALS OF MATHEMATICS | 2014年 / 180卷 / 01期

关键词：

HASSE PRINCIPLE; WEAK APPROXIMATION; DESCENT; FIBRATIONS; BUNDLES;

D O I：

10.4007/annals.2014.180.1.8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For any pencil of conics or higher-dimensional quadrics over Q, with all degenerate fibres defined over Q, we show that the Brauer-Manin obs truction controls weak approximation. The proof is based on the Hasse principle and weak approximation for some special intersections of quadrics overQ, which is a consequence of recent advances in additive combinatorics.

引用

页码：381 / 402

页数：22

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