We present a method for calculating the Brauer group of a surface given by a diagonal equation in projective space. For diagonal quartic surfaces with coefficients in , we determine the Brauer groups over and .
In memory of Sir Peter Swinnerton-Dyer
"Cohomology and the Brauer groups of diagonal surfaces." Duke Math. J. 171 (6) 1299 - 1347, 15 April 2022. https://doi.org/10.1215/00127094-2021-0029