The Brauer-group conjecture for stable quiver moduli

Let $Q$ be a quiver, let ${\bf d}$ be a dimension type for which stable representations exist, and let $M_{\bf d}^{\rm sst}(Q)$ denote the corresponding moduli space of stable representations. Write $g({\bf d})$ for the greatest common divisor of the entries of ${\bf d}$. Brauer-group conjecture. The Brauer group

$$\operatorname{Br}(M_{\bf d}^{\rm sst}(Q))$$

is cyclic of order $g({\bf d})$, and the class of every $P_{\bf n}$ for ${\bf n}\not=0$ is a generator. This conjecture predicts the precise obstruction to the existence of tautological families on stable quiver moduli; the paper presents it as motivated by experiments, and its general status is not resolved in the supplied text.