On the Brauer group of diagonal quartic surfaces

Details On the Brauer group of diagonal quartic surfaces On the Brauer group of diagonal quartic surfaces

2009-12-15

arxiv.org/abs/0912.2865v2

Mathematics

Algebraic Geometry

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

Scientific paper

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.

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