Brauer-Manin Obstructions on Generalized Kummer Varieties

I will discuss the Brauer-Manin obstruction, a generalization of the local-global principle in arithmetic geometry. This idea is used to decide if polynomial equations have rational solutions. It arises from a cohomological invariant of a variety called the Brauer group and we can use this group to find obstructions to rational points. Then, I will discuss my work on the Brauer-Manin obstruction of generalized Kummer varieties. These are varieties arising from finite order quotients of abelian varieties and I prove that the Brauer-Manin obstruction on these varieties can only come from elements of the Brauer group of certain orders. This is motivated by the work of Skorobogatov and Zarhin.