On the Brauer group of diagonal quartic surfaces

被引：25

作者：

Ieronymou, Evis ^{[1
]}

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

Zarhin, Yuri G. ^{[4
,5
]}

机构：

[1] Ecole Polytech Fed Lausanne, EPFL SFB IMB CSAG, Stn 8, CH-1015 Lausanne, Switzerland

[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

[4] Penn State Univ, Dept Math, University Pk, PA 16802 USA

[5] Russian Acad Sci, Inst Math Problems Biol, Pushchino 142292, Moscow Region, Russia

来源：

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 2011年 / 83卷

关键词：

D O I：

10.1112/jlms/jdq083

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain an easy sufficient condition for the Brauer group of a diagonal quartic surface D over Q to be algebraic. We also give an upper bound for the order of the quotient of the Brauer group of D by the image of the Brauer group of Q. The proof is based on the isomorphism of the Fermat quartic surface with a Kummer surface due to Mizukami.

引用

页码：659 / 672

页数：14

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