Title: Brauer-Manin obstructions requiring arbitrarily many Brauer classes

Abstract:
The Brauer-Manin obstruction is a method to show that a projective
variety has no rational points, even though it has points over every
completion of the rationals. It is defined in terms of the Brauer group
of the variety (and uses a basic fact from class field theory). In most
examples in the literature, the contradiction is obtained by looking at
just one element ("Brauer class") of the Brauer group. We show that
there are examples needing arbitrarily many Brauer classes to derive the
absence of rational points.

This is joint work with Jennifer Berg, Carlo Pagano, Bjorn Poonen,
Nicholas Triantafillou, Bianca Viray and Isabel Vogt.