Odd torsion Brauer elements and arithmetic of diagonal quartic surfaces over number fields

Evis Ieronymou

Published 2022-09-30Version 1

We use some recent advances in the local evaluation of Brauer elements in order to study in some detail the role played by odd torsion elements of the Brauer group in the arithmetic of diagonal quartic surfaces over arbitrary number fields. We also note a systematic way to produce K3 surfaces over \Q_2 with good reduction and a non-trivial 2-torsion element of the Brauer group with Swan conductor zero.