Brauer groups of diagonal quartic surfaces

被引：19

作者：

Bright, M ^{[1
]}

机构：

[1] Univ Liverpool, Dept Math Sci, Liverpool L69 7ZL, Merseyside, England

来源：

JOURNAL OF SYMBOLIC COMPUTATION | 2006年 / 41卷 / 05期

基金：

英国工程与自然科学研究理事会;

关键词：

Brauer-Manin obstruction; Brauer group; K3; surfaces;

D O I：

10.1016/j.jsc.2005.10.001

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We describe explicit methods of exhibiting elements of the Brauer groups of diagonal quartic surfaces. Using these methods, we compute the algebraic Brauer-Manin obstruction in two contrasting examples. In the second example, the obstruction is found to be trivial but a computer search reveals no points of small height on the surface. (c) 2005 Elsevier Ltd. All rights reserved.

引用

页码：544 / 558

页数：15

共 22 条

[1]

Bernstein DJ, 2001, MATH COMPUT, V70, P389, DOI 10.1090/S0025-5718-00-01219-9

[2] The Magma algebra system .1. The user language [J].

Bosma, W ;

Cannon, J ;

Playoust, C .

JOURNAL OF SYMBOLIC COMPUTATION, 1997, 24 (3-4) :235-265

[3] Computing the Brauer-Manin obstructions [J].

Bright, M ;

Swinnerton-Dyer, P .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2004, 137 :1-16

[4]

BRIGHT MJ, 2002, SOME COMPUTATIONAL R

[5] Hasse principle for pencils of curves of genus one whose Jacobians have rational 2-division points [J].

Colliot-Thelene, JL ;

Skorobogatov, AN ;

Swinnerton-Dyer, P .

INVENTIONES MATHEMATICAE, 1998, 134 (03) :579-650

[6]

COLLIOTTHELENE JL, 1994, J REINE ANGEW MATH, V453, P49

[7]

COLLIOTTHELENE JL, 1980, J REINE ANGEW MATH, V320, P150

[8]

Cremona JE, 2003, MATH COMPUT, V72, P1417, DOI 10.1090/S0025-5718-02-01480-1

[9]

Grothendieck A., 1968, 509 EXPOSES COHOMOLO, P46

[10]

MAGMA, 2003, MAGMA COMPUTATIONAL

← 1 2 3 →