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arXiv · 0911.1268

Diagonal quartic surfaces and transcendental elements of the Brauer group

Evis Ieronymou
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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 transendental 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.

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Evis Ieronymou. 2009-11-06. Diagonal quartic surfaces and transcendental elements of the Brauer group. https://arxiv.org/abs/0911.1268

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