Alexei Skorobogatov

Etale cohomology of abelian varieties, and applications to the Brauer group of K3 surfaces

Abstract :

The Hochschild-Serre spectral sequence that computes the étale cohomology of an abelian variety with finite coefficients completely generates. This applies to the computation of the Brauer group of an abelian variety. In dimension 2 one can obtain upper bounds for the Brauer group of the associated Kummer surface, and those can be used to produce examples of diagonal quartic surfaces with trivial Brauer group.

Most of these results are joint with Yuri Zarhin and Evis Ieronymou.