Diagonal quartic surfaces and transcendental elements of the Brauer group

Abstract

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.

Locations

• Journal of the Institute of Mathematics of Jussieu - View
• arXiv (Cornell University) - View - PDF
• Infoscience (Ecole Polytechnique Fédérale de Lausanne) - View - PDF