Related papers: Brauer groups for quiver moduli

We establish a formula for computing the unramified Brauer group of tame conic bundle threefolds in characteristic 2. The formula depends on the arrangement and residue double covers of the discriminant components, the latter being governed…

Let ${\mathcal P}{\mathcal M}^\alpha_s$ be a moduli space of stable parabolic vector bundles of rank $n \geq 2$ and fixed determinant of degree $d$ over a compact connected Riemann surface $X$ of genus $g(X) \geq 2$. If $g(X) = 2$, then we…

We give an explicit description of $\overline{\mathcal{M}}_{1,2}$ as a weighted blow-up of a weighted projective stack. We use this description to compute the Brauer group of $\overline{\mathcal{M}}_{1,2;S}$ over any base scheme $S$ where 6…

We study the Brauer groups of affine surfaces that are complements of singular hyperplane sections of smooth cubic surfaces over a field $k$ of characteristic $0$. We determine the Brauer group over the algebraic closure as a Galois module…

We produce a partial compactification of the variety given by P(t)=N_{K/k}(\mathbf z) whose Brauer group coincides with the unramified Brauer group, where K is an \'etale k-algebra and P(t)\in k[t] is a nonconstant polynomial. Then we…

We consider representation spaces of quivers, together with their base change action, and classify the spherical varieties among them.

For a given small binary dihedral group G we use the classification of G-graphs to describe explicitly G-Hilb(C^2) by giving an affine open cover of M(Q,R), the moduli space of stable quiver representations.

In this article, we study the Schur mutiplier of the discrete as well as the finite Heisenberg groups and their t-variants. We describe the representation groups of these Heisenberg groups and through these give a construction of their…

In this paper, we determine the structure and representation theory of the Brauer algebra associated to a complex reflection group (here called the Brauer-Chen algebra), defined by Chen in 2011. We prove that it is semisimple and provide a…

We construct moduli spaces of representations of quivers over arbitrary schemes and show how moduli spaces of pointed curves of genus zero like the Grothendieck-Knudsen moduli spaces $\overline{M}_{0,n}$ and the Losev-Manin moduli spaces…

Using profinite Galois descent, we compute the Brauer group of the $K(1)$-local category relative to Morava E-theory. At odd primes this group is generated by a cyclic algebra formed using any primitive $(p-1)$st root of unity, but at the…

We compute the vertical unramified Brauer group of the Galois normic bundles, which are given by $\mathrm{N}_{K/k}(\mathbf{z})=P(x)$. Our main result gives combinatorial formulas for the vertical unramified Brauer groups in terms of the…

In this paper we introduce a method to obtain algebraic information using arithmetic one in the study of tori and their principal homogeneous spaces. In particular, using some results of the authors with Tingyu Lee, we determine the…

The Brauer group of a commutative ring is an important invariant of a commutative ring, a common journeyman to the group of units and the Picard group. Burnside rings of finite groups play an important role in representation theory, and…

We define a one-dimensional family of "Euler" stability conditions on $\mathbb{P}^n$ which are conjectured to converge to Gieseker stability for coherent sheaves. Here, we focus on ${\mathbb P}^3$, first identifying Euler stability…

We study the conjugacy classes of the classical affine groups. We derive generating functions for the number of classes analogous to formulas of Wall and the authors for the classical groups. We use these to get good upper bounds for the…

We study the spaces of stable real and quaternionic vector bundles on a real algebraic curve. The basic relationship is established with unitary representations of an extension Z/2 by the fundamental group. By comparison with the space of…

We describe two methods for computing $p$-modular Brauer character tables for groups of Lie type $G(p^f)$ in defining characteristic $p$, assuming that the ordinary character table of $G(p^f)$ is known, and the weight multiplicities of the…

We determine explicitly the stable homotopy groups of Moore spaces up to the range 7, using an equivalence of categories which allows to consider each Moore space as an exact couple of $\mathbb Z$-modules.

We compute the first, second, third, and fifth rational cohomology groups of the moduli space of stable n-pointed genus g curves, for all g and n, using (mostly) algebro-geometric techniques.