On the Brauer group of diagonal quartic surfaces

Abstract

We obtain an easy sufficient condition for the Brauer group of a diagonal quartic surface D over Q to be algebraic. We also give an upper bound for the order of the quotient of the Brauer group of D by the image of the Brauer group of Q. The proof is based on the isomorphism of the Fermat quartic surface with a Kummer surface due to Masumi Mizukami.

Appendix "The Fermat quartic as a Kummer surface (after Mizukami)", by Sir Peter Swinnerton-Dyer