Rachel Newton

Relevant primes for the Brauer—Manin obstruction

The local-global approach to the study of rational points on varieties over number fields begins by embedding the set of rational points on a variety X into the set of its adelic points. Then the Brauer—Manin pairing cuts out a subset of the adelic points that contains the closure of the rational points. Computing the Brauer—Manin pairing involves evaluating elements of the Brauer group of X at p-adic points. In this talk, I will discuss which primes are relevant for the Brauer—Manin obstruction, meaning that there is an element of the Brauer group with non-constant evaluation on p-adic points. I will present results from two collaborations: one with Martin Bright, and one with Emiliano Ambrosi and Margherita Pagano.