Ieronymou, Evis2011-12-162011-12-162011-12-16201010.1017/S1474748010000149https://infoscience.epfl.ch/handle/20.500.14299/75128WOS:000282620200005We 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.diagonal quartic surfacesBrauer groupBrauer-Manin obstructionweak approximationHasse PrincipleElliptic-CurvesGenus OneVarietiesJacobiansDescentPencilsPointstext::journal::journal article::research article