On the Brauer group of diagonal surfaces
Alexei Skorobogatov (Imperial College London )
Wednesday 12th February, 2020 16:00-17:00 Maths 311B
Using work of Pham and Looijenga on the complex cohomology of Fermat varieties, and work of Weil, Katz, Shioda and Ulmer on the associated Galois representation, we propose a method of calculating the Brauer group of a surface given by a diagonal equation over a number field. In the case of quartic diagonal surfaces with rational coefficients we determine the Brauer group modulo the Brauer group of the ground field k, in the case when k=Q or k=Q(i). This is a joint work with Damián Gvirtz.