Relative Brauer groups of curves
Michigan State University.
The relative Brauer group of function fields of curves has recently generated much interest. We will discuss historical interest in this circle of ideas followed by recent developments. We will then discuss our recent work (together with Aaron Levin). One consequence of our work is that over a global field $K$, given a square-free integer $\ell$ and a finitely generated $\ell$-torsion subgroup G of the Brauer group of $K$, we construct a smooth projective curve with minimal gonality whose relative Brauer group contains G. We will also discuss the relationship with representations of weighted Clifford algebras.