Brauer-Manin obstructions on Kummer Surfaces of CM elliptic curves Mohamed Tawfik, King's College London This talk will be on Zoom. Contact Paul Fili for the link.
Abstract: 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 a generator of this group. 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.
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