The Brauer group of cubic surfaces
The Brauer group of cubic surfaces
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立方体表面的布劳尔群
DOI：
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发表时间：
1993
影响因子：
0.8
通讯作者：
Sir Peter Swinnerton
中科院分区：
文献类型：
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作者：
Sir Peter Swinnerton
1.设V是定义在代数数域k上的非奇异有理曲面。有一个标准的猜想，唯一的障碍，哈塞原则和弱逼近的V是布劳尔-马宁障碍。计算这些的先决条件是V的布劳尔群的知识;确实有一个这样的障碍，但可能是微不足道的，对应于每个元素的Br V/Br k。因为k是代数数域，自然注入是同构;所以计算Brauer-Manin阻塞的第一步是计算有限群H1（k），Pic。
1. Let V be a non-singular rational surface defined over an algebraic number field k. There is a standard conjecture that the only obstructions to the Hasse principle and to weak approximation on V are the Brauer–Manin obstructions. A prerequisite for calculating these is a knowledge of the Brauer group of V; indeed there is one such obstruction, which may however be trivial, corresponding to each element of Br V/Br k. Because k is an algebraic number field, the natural injection is an isomorphism; so the first step in calculating the Brauer–Manin obstruction is to calculate the finite group H1 (k), Pic .