Related papers: Non-commutative derived moduli prestacks

Inspired by the commutator and anticommutator algebras derived from algebras graded by groups, we introduce noncommutatively graded algebras. We generalize various classical graded results to the noncommutatively graded situation concerning…

We introduce the notion of non commutative truncated polynomial extension of an algebra A. We study two families of these extensions. For the first one we obtain a complete classification and for the second one, which we call upper…

In arXiv:2407.11958, a moduli stack parametrizing $I$--indexed diagrams of Higgs bundles over a base stack $X$ was constructed for any finite simplicial set $I$, inspiring speculations about extending the non-Abelian Hodge correspondence to…

Derived mapping stacks are a fundamental source of examples of derived enhancements of classical moduli problems. For instance, they appear naturally in Gromov-Witten theory and in some branches of geometric representation theory. In this…

We introduce a category of noncommutative bundles. To establish geometry in this category we construct suitable noncommutative differential calculi on these bundles and study their basic properties. Furthermore we define the notion of a…

Motivated by applications in moduli theory, we introduce a flexible and powerful language for expressing lower bounds on relative dimension of morphisms of schemes, and more generally of algebraic stacks. We show that the theory is robust…

We explain how any Artin stack $\mathfrak{X}$ over $\mathbb{Q}$ extends to a functor on non-negatively graded commutative cochain algebras, which we think of as functions on Lie algebroids or stacky affine schemes. There is a notion of…

In this review article the construction of first order coordinate differential calculi on finitely generated and finitely related associative algebras are considered and explicit construction of the bimodule of one form over such algebras…

These are expanded notes from some talks given during the fall 2002, about ``homotopical algebraic geometry'' (HAG) with special emphasis on its applications to ``derived algebraic geometry'' (DAG) and ``derived deformation theory''. We use…

Given a Hopf algebra H, we study modules and bimodules over an algebra A that carry an H-action, as well as their morphisms and connections. Bimodules naturally arise when considering noncommutative analogues of tensor bundles. For…

The central structure in various versions of noncommutative geometry is a differential calculus on an associative algebra. This is an analogue of the calculus of differential forms on a manifold. In this short review we collect examples of…

We give a general construction of extended moduli spaces of topological D-branes as non-commutative algebraic varieties. This shows that noncommutative symplectic geometry in the sense of Kontsevich arises naturally in String Theory.

The underlying algebra for a noncommutative geometry is taken to be a matrix algebra, and the set of derivatives the adjoint of a subset of traceless matrices. This is sufficient to calculate the dual 1-forms, and show that the space of…

We define a new type of Hall algebras associated e.g. with quivers with polynomial potentials. The main difference with the conventional definition is that we use cohomology of the stack of representations instead of constructible sheaves…

We give a systematic construction of semiorthogonal decompositions of derived categories of coherent sheaves on quasi-smooth derived algebraic stacks over $\mathbb{C}$, where the summands are subcategories defined by weight conditions, and…

We develop a theory of good moduli spaces for derived Artin stacks, which naturally generalizes the classical theory of good moduli spaces introduced by Alper. As such, many of the fundamental results and properties regarding good moduli…

We show that a semi-commutative Galois extension of a unital associative algebra can be endowed with the structure of a graded q-differential algebra. We study the first and higher order noncommutative differential calculus of…

In recent years, researchers have discovered various large algebraic structures that have surprising finiteness properties, such as FI-modules and Delta-modules. In this paper, we add another example to the growing list: we show that…

We construct shifted symplectic derived enhancements on rigidified moduli spaces of sheaves on Calabi-Yau varieties of dimension at least two. More generally, we prove that any $B\mathbb{G}_m$-action on a non-positively-shifted symplectic…

We propose a simple approach to formal deformations of associative algebras. It exploits the machinery of multiplicative coresolutions of an associative algebra A in the category of A-bimodules. Specifically, we show that certain…