Abelian $n$-division fields of elliptic curves and Brauer groups of product Kummer & abelian surfaces

Anthony Várilly-Alvarado, Bianca Viray

Let $Y$ be a principal homogeneous space of an abelian surface, or a K3 surface, over a finitely generated extension of $\mathbb{Q}$. In 2008, Skorobogatov and Zarhin showed that t…