Related papers: Artin algebraization and quotient stacks

Let $G$ be a connected reductive group acting on a complex vector space $V$ and projective space ${\mathbb P}V$. Let $x\in V$ and ${\cal H}\subseteq {\cal G}$ be the Lie algebra of its stabilizer. Our objective is to understand points…

Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…

In this note, we use give some algebraic applications of a previous result by the author which compares the deformations parameterized by the Maurer-Cartan elements of a differential graded Lie algebra, and a differential graded Lie…

Diagram algebras (e.g. graded braid groups, Hecke algebras, Brauer algebras) arise as tensor power centralizer algebras, algebras of commuting operators for a Lie algebra action on a tensor space. This work explores centralizers of the…

We refine and advance the study of the local structure of idempotent finite algebras started in [A.Bulatov, The Graph of a Relational Structure and Constraint Satisfaction Problems, LICS, 2004]. We introduce a graph-like structure on an…

The Ablowitz-Ladik system, being one of the few integrable nonlinear lattices, admits a wide class of analytical solutions, ranging from exact spatially localised solitons to rational solutions in the form of the spatiotemporally localised…

We prove structure theorems for algebraic stacks with a reductive group action and a dense open substack isomorphic to a horospherical homogeneous space, and thereby obtain new examples of algebraic stacks which are global quotient stacks.…

Let $G$ be a reductive algebraic group and let $Z$ be the stabilizer of a nilpotent element $e$ of the Lie algebra of $G$. We consider the action of $Z$ on the flag variety of $G$, and we focus on the case where this action has a finite…

Using formal-local methods, we prove that a separated and normal tame Artin surface has the resolution property. By proving that normal tame Artin stacks can be rigidified, we ultimately reduce our analysis to establishing the existence of…

These are expended notes of my talk at the summer institute in algebraic geometry (Seattle, July-August 2005), whose main purpose is to present a global overview on the theory of higher and derived stacks. This text is far from being…

This is an introduction to some aspects of Fomin-Zelevinsky's cluster algebras and their links with the representation theory of quivers and with Calabi-Yau triangulated categories. It is based on lectures given by the author at summer…

We prove Artin's axioms satisfy a compatibility for composition of 1-morphisms of stacks in groupoids. Consequently, some natural stacks in groupoids are algebraic, including a common generalization of Vistoli's Hilbert stack and the stack…

We will study the relationship of quite different object in the theory of artin algebras, namely Auslander-regular rings of global dimension two, torsion theories, $\tau$-categories and almost abelian categories. We will apply our results…

In this paper we consider the Brauer groups of algebraic stacks and GIT quotients: the only algebraic stacks we consider in this paper are quotient stacks [X/G], where X is a smooth scheme of finite type over a field k, and G is a linear…

We give a sufficient criterion for the Chow or algebraic bordism groups of an algebraic stack, localized at a set of Chern classes of line bundles, to be concentrated in some closed substack. This is a vast generalization of the torus…

We use operator algebras and operator theory to obtain new result concerning Berezin quantization of compact K\"ahler manifolds. Our main tool is the notion of subproduct systems of finite-dimensional Hilbert spaces, which enables all…

Let \pi : X -> S be a morphism of algebraic stacks that is locally of finite presentation with affine stabilizers. We prove that there is an algebraic S-stack, the Hilbert stack, parameterizing proper algebraic stacks mapping quasi-finitely…

Quillen's localization theorem is well known as a fundamental theorem in the study of algebraic K-theory. In this paper, we present its arithmetic analogue for the equivariant K-theory of arithmetic schemes, which are endowed with an action…

Decomposition classes provide a way of partitioning the Lie algebras of an algebraic group into equivalence classes based on the Jordan decomposition. In this paper, we investigate the decomposition classes of the Lie algebras of connected…

In 1979, Lusztig proposed a cohomological construction of supercuspidal representations of reductive $p$-adic groups, analogous to Deligne-Lusztig theory for finite reductive groups. In this paper we establish a new instance of Lusztig's…