turkmath.org

We discuss Brauer-Manin obstructions on Kummer surfaces of products of certain CM elliptic curves. We start by putting necessary and sufficient conditions on these surfaces to get a non-trivial transcendental Brauer group, then we find the construction of these groups. Further, using a theorem by Harpaz and Skorobogatov, we show that a non-trivial element of order 5 of the transcendental Brauer group always gives rise to Brauer-Manin obstruction to weak approximation on these surfaces. Finally, we show that for most cases there is no obstruction coming from the algebraic part.