On the Brauer group of diagonal surfaces

Alexei Skorobogatov (Imperial College London )

Wednesday 12th February, 2020 16:00-17:00 Maths 311B

Abstract

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.

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