Related papers: Morse decomposition for D-module categories on sta…

We study the Borel-Moore homology of stacks of representations of preprojective algebras $\Pi_Q$, via the study of the DT theory of the undeformed 3-Calabi-Yau completion $\Pi_Q[x]$. Via a result on the supports of the BPS sheaves for…

Given Y a non-compact manifold or orbifold, we define a natural subspace of the cohomology of Y called the narrow cohomology. We show that despite Y being non-compact, there is a well-defined and non-degenerate pairing on this subspace. The…

We identify a class of "quasi-compact semi-separated" (qcss) twisted presheaves of algebras A for which well-behaved Grothendieck abelian categories of quasi-coherent modules Qch(A) are defined. This class is stable under algebraic…

Let G be a split semisimple linear algebraic group over a field k0. Let E be a G-torsor over a field extension k of k0. Let h be an algebraic oriented cohomology theory in the sense of Levine-Morel. Consider a twisted form E/B of the…

For a coherent filtered D-module we show that the dual of each graded piece over the structure sheaf is isomorphic to a certain graded piece of the ring-theoretic local cohomology complex of the graded quotient of the dual of the filtered…

For a reductive group $G$, Harder-Narasimhan theory gives a structure theorem for principal $G$ bundles on a smooth projective curve $C$. A bundle is either semistable, or it admits a canonical parabolic reduction whose associated Levi…

Using the new approach to analytic geometry developed by Clausen and Scholze by means of condensed mathematics, we prove that for every affinoid analytic adic space $X$, pseudocoherent complexes, perfect complexes, and finite projective…

We study twisted D-modules on the weighted projective stacks. We determine for which values of the twist and the weight the global section functor is an equivalence, thus, proving a version of Beilinson-Bernstein Localisation Theorem.

Given a reductive group G, Kostant and Kumar defined a nil Hecke algebra that may be viewed as a degenerate version of the double affine nil Hecke algebra introduced by Cherednik. In this paper, we construct an isomorphism of the spherical…

In this Part II, D(10.2), of D(10), we take D(10.1) (arXiv:1302.2054 [math.AG]) as the foundation to define the notion of $Z$-semistable morphisms from general Azumaya nodal curves, of genus $\ge 2$, with a fundamental module to a…

In this paper, we introduce a notion of weight r pseudo-coherent Modules associated to a regular closed immersion i:Y -> X of codimension r, and prove that there is a canonical derived Morita equivalence between the DG-category of perfect…

In this paper, we present a new connection between representation theory of noncommutative hypersurfaces and combinatorics. Let $S$ be a graded ($\pm 1$)-skew polynomial algebra in $n$ variables of degree $1$ and $f =x_1^2 + \cdots +x_n^2…

Let $\mathcal{X}$ be a smooth Deligne-Mumford stack which is generically a scheme and has quasi-projective coarse moduli. If $\mathcal{X}$ has elementary Abelian 2-group stabilizers and the coarse moduli of the inertia stack is smooth, we…

Continuing our previous work on graded twisting of Hopf algebras and monoidal categories, we introduce a graded twisting construction for equivariant comodule algebras and module categories. As an example we study actions of quantum…

We compactify the moduli stack of maps from curves to certain quotient stacks $\mathcal{X}=[W/G]$ with a projective good moduli space, extending previous results from quasimap theory. For doing so, we introduce a new birational…

We develop a version of Hodge theory for a large class of smooth formally proper quotient stacks $X/G$ analogous to Hodge theory for smooth projective schemes. We show that the noncommutative Hodge-de Rham sequence for the category of…

On a smooth projective variety with k ample line bundles, we denote by Z the complete intersection subvariety defined by generic sections. We define the twisted quantum D-module which is a vector bundle with a flat connection, a flat…

In this brief postscript to our paper "Integral transforms and Drinfeld centers in derived algebraic geometry", we describe a Morita equivalence for derived, categorified matrix algebras implied by theory developed since its appearance. We…

We introduce stacks classifying \'etale germs of pointed n-dimensional varieties. We show that quasi-coherent sheaves on these stacks are universal D- and O-modules. We state and prove a relative version of Artin's approximation theorem,…

We introduce a notion of morphism of CohFT algebras, based on the analogy with A-infinity morphisms. We discuss a "quantization" of the classical Kirwan morphism to a morphism of CohFT algebras from the equivariant quantum cohomology of a…