Diagonal quartic surfaces and transcendental elements of the Brauer group
Diagonal quartic surfaces and transcendental elements of the Brauer group
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对角四次曲面和布劳尔群的超越元
DOI：
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发表时间：
2009
影响因子：
0.9
通讯作者：
Evis Ieronymou
中科院分区：
文献类型：
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作者：
Evis Ieronymou
摘要我们在一个对角四次曲面的函数场上，展示了代表其Brauer群的2-扭转部分的复数上的中心简单代数。研究了数域上对角四次曲面的Brauer群的2-初等部分是否为代数的，并给出了其为代数的充分条件。在最后一节中，我们给出了在特定对角线四次曲面上的一个超越类对弱逼近的阻碍，这种阻碍不能用代数Brauer群来解释，在这种情况下，代数Brauer群就是常数代数。
ABSTRACT We exhibit central simple algebras over the function field of a diagonal quartic surface over the complex numbers that represent the 2-torsion part of its Brauer group. We investigate whether the 2-primary part of the Brauer group of a diagonal quartic surface over a number field is algebraic and give sufficient conditions for this to be the case. In the last section we give an obstruction to weak approximation due to a transcendental class on a specific diagonal quartic surface, an obstruction which cannot be explained by the algebraic Brauer group which in this case is just the constant algebras.