Odd order Brauer--Manin obstruction on diagonal quartic surfaces

Abstract

We determine the odd order torsion subgroup of the Brauer group of diagonal quartic surfaces over the field of rational numbers. We show that a non-constant Brauer element of odd order always obstructs weak approximation but never the Hasse principle.

24 pages

References in corpus (1)

• On p-torsion of p-adic elliptic curves with additive reduction