# Fortnightly links (61)

Minseon Shin: The cohomological Brauer group of a torsion $\mathbb{G}_{\mathfrak{m}}$-gerbe is a fun preprint explaining how the Brauer–Severi scheme of a Brauer class behaves in the same way as the $\mathbb{G}_{\mathfrak{m}}$-gerbe associated to this class. Indeed, for $\alpha\in\operatorname{Br}'(X)$ it is a classical fact due to Gabber that $\operatorname{Br}'(\operatorname{BS}(\alpha))$ is the quotient of $\operatorname{Br}'(X)$ by the class $\alpha$, and it turns out that the same is true for $\operatorname{Br}'(\mathcal{X})$, where $\mathcal{X}$ is the $\mathbb{G}_{\mathfrak{m}}$-gerbe over $X$ associated to $\alpha$.

RRAGE: Ragnar's ramifications in algebra and geometry emerging workshop is a workshop dedicated to the work of Ragnar Buchweitz. I don't often announce conferences on my blog (see ncag.info for this), but for Ragnar I am making an exception.

George Dimitrov, Ludmil Katzarkov: Non-commutative curve-counting invariants introduces the idea of counting Kronecker quivers inside triangulated categories. It turns out that this can shed light on the

*Markov conjecture*(stated by Frobenius actually, in 1913), which says that an integer solution $(a,b,c)$ with $a