Related papers: Rational points of quiver moduli spaces
Torus fixed points of quiver moduli spaces are given by stable representations of the universal (abelian) covering quiver. As far as the Kronecker quiver is concerned they can be described by stable representations of certain bipartite…
We study algebraic actions of finite groups of quiver automorphisms on moduli spaces of quiver representations. We decompose the fixed loci using group cohomology and we give a modular interpretation of each component. As an application, we…
It is shown that rational points over finite fields of moduli spaces of stable quiver representations are counted by polynomials with integer coefficients. These polynomials are constructed recursively using an identity in the Hall algebra…
We compute the Brauer groups of several moduli spaces of stable quiver representations.
We study representation finite $K$-rational quivers over fields of characteristic $0$ and their indecomposable representations, exploiting that all Brauer obstructions for descent of representations are trivial in this case. Contrasting the…
The fixed point set under a natural torus action on projectivized moduli spaces of simple representations of quivers is described. As an application, the Euler characteristic of these moduli is computed.
We construct and study the moduli of continuous representations of a profinite group with integral $p$-adic coefficients. We present this moduli space over the moduli space of continuous pseudorepresentations and show that this morphism is…
We use categorical method and birational geometry to study moduli spaces of quiver representations. From certain "representable" functor, we construct a birational transformation from the moduli space of representations of one quiver to…
For an algebraically closed field K, let G be a finite abelian group of K-linear automorphisms of a finite-dimensional path algebra KQ of a quiver Q. Under certain assumptions on the action of G, we show the existence of a certain kind of…
This article describes some complex-analytic aspects of the moduli space of the finite-dimensional complex representations of a finite quiver, which are stable with respect to a fixed rational weight. We construct a natural structure of a…
An introduction to moduli spaces of representations of quivers is given, and results on their global geometric properties are surveyed. In particular, the geometric approach to the problem of classification of quiver representations is…
We compute rational equivariant Chow rings with respect to a torus of quiver moduli spaces. We derive a presentation in terms of generators and relations, use torus localization to identify it as a subring of the Chow ring of the fixed…
Let G be a Lie group and Q a quiver with relations. In this paper, we define G-valued representations of Q which directly generalize G-valued representations of finitely generated groups. Although as G-spaces, the G-valued quiver…
We consider the tensor product of modules over the polynomial algebra corresponding to the usual tensor product of linear operators. We present a general description of the representation ring in case the ground field k is perfect. It is…
We study moduli spaces and moduli stacks for representations of associative algebras in Azumaya algebras, in rather general settings. We do not impose any stability condition and work over arbitrary ground rings, but restrict attention to…
We survey some results on counting the rational points of moduli spaces of quiver representations. We then make generalizations to Grassmannians and flags of quiver representations. These results have nice applications to the cluster…
This article surveys modularity, level raising and level lowering questions for two-dimensional representations modulo prime powers of the absolute Galois group of the rational numbers. It contributes some new results and describes…
Extending work of Klyachko and Perling, we develop a combinatorial description of pure equivariant sheaves of any dimension on an arbitrary nonsingular toric variety $X$. Using geometric invariant theory (GIT), this allows us to construct…
These lecture notes consist of an introduction to moduli spaces in algebraic geometry, with a strong emphasis placed on examples related to the theory of quiver representations. The goal is to provide the background necessary to understand…
For a fixed mod $p$ automorphic Galois representation, $p$-adic automorphic Galois representations lifting it determine points in universal deformation space. In the case of modular forms and under some technical conditions, B\"{o}ckle…