Diagonal quartic surfaces and transcendental elements of the Brauer group

Details Diagonal quartic surfaces and transcendental elements of the Brauer group Diagonal quartic surfaces and transcendental elements of the Brauer group

2009-11-06

arxiv.org/abs/0911.1268v1

Mathematics

Number Theory

29 pages

Scientific paper

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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