Diagonal Quartic Surfaces And Transcendental Elements Of The Brauer Group

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.

Published in:
Journal Of The Institute Of Mathematics Of Jussieu, 9, 769-798

 Record created 2011-12-16, last modified 2018-03-17

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