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Diagonal quartic surfaces and transcendental elements of the Brauer group

Published online by Cambridge University Press:  28 May 2010

Evis Ieronymou
Affiliation:
École Polytechnique Fédérale de Lausanne, EPFL-SFB-IMB-CSAG, Station 8, CH-1015, Lausanne, Switzerland (evis.ieronymou@epfl.ch)

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.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2010

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