### Brauer-Manin obstructions for Kummer surfaces

Linfoot Number Theory Seminar

21st February 2024, 11:00 am – 12:00 pm

Fry Building, 2.04

We start by introducing Brauer-Manin obstructions to local-global principles over varieties. We then move to some of the known literature on Brauer-Manin obstructions for Kummer surfaces of products of elliptic curves. We finally present our work on some of the special cases where we calculate the Brauer group of a Kummer surface X=Kum(E \times E') of a product of CM elliptic curves E and E', where End(E)=End(E')=Z[\zeta_3], and show that a non-trivial 5-torsion element of the transcendental Brauer group gives rise to Brauer Manin obstruction to weak approximation for X.

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