Related papers: Dimensional reduction in cohomological Donaldson-T…
The affinization morphism for the stack $\mathfrak{M}(\Pi_Q)$ of representations of a preprojective algebra $\Pi_Q$ is a local model for the morphism from the stack of objects in a general 2-Calabi-Yau category to the good moduli space. We…
We discuss a connection between coherent duality and Verdier duality via a Gersten-type complex of sheaves on real schemes, and show that this construction gives a dualizing object in the derived category, which is compatible with the…
We prove a motivic integral identity relating the motivic Behrend function of a $(-1)$-shifted symplectic stack to that of its stack of graded points. This generalizes analogous identities for moduli stacks of objects in…
We consider a hyperplane arrangement in $\mathbb{C}^n$ defined over $\mathbb{R}$, and the associated natural stratification of $\mathbb{C}^n$. The category of perverse sheaves smooth with respect to this stratification was described by…
Supersymmetric D-branes supported on the complex two-dimensional base $S$ of the local Calabi-Yau threefold $K_S$ are described by semi-stable coherent sheaves on $S$. Under suitable conditions, the BPS indices counting these objects (known…
In this paper, we complete the nonabelian Hodge theory (NAHT) triangle of isomorphisms for stacks between the Borel-Moore homologies of the Dolbeault, Betti, and de Rham moduli stacks. We first explain how to realise the category of…
We prove that the homotopy algebraic K-theory of tame quasi-DM stacks satisfies cdh-descent. We apply this descent result to prove that if X is a Noetherian tame quasi-DM stack and i < -dim(X), then K_i(X)[1/n] = 0 (resp. K_i(X, Z/n) = 0)…
We show that the cohomology of the structure sheaf of smooth and proper schemes over a complete non-archimedean field $K$ of characteristic zero, can be refined to an $\mathbf{A}^1$-invariant cohomology theory of smooth (not necessarily…
We present the construction and properties of a self-dual perverse sheaf S_0 whose cohomology fulfills some of the requirements of String theory as outlined by T. Hubsch in hep-th/9612075. The construction of this S_0 utilizes techniques…
In this short note, we observe that Theorem 3.1 in arXiv:1508.00682 for semiorthogonal indecomposability of the derived category of smooth DM stacks based on the canonical bundle can be extended to the case of projective varieties with…
We construct twisted $\mathcal{D}$-modules on the projective line $\mathbb{P}^1$ that are equivariant for the action of the diagonal torus subgroup of $SL_2$. In the most interesting case these arise as extensions from local systems on…
Inspired by the work of Pomoni-Yan-Zhang in String Theory, we introduce the moduli space of tetrahedron instantons as a Quot scheme and describe it as a moduli space of quiver representations. We construct a virtual fundamental class and…
Thin homotopies, introduced by Caetano-Picken, serve to axiomatize the holonomy of connections on principal bundles. This approach has been generalized to higher non-abelian bundles with connection through transport functors and higher…
We introduce an original notion of extra-fine sheaf on a topological space, and a variant (hyper-extra-fine) for which \v{C}ech cohomology in strictly positive degree vanishes. We provide a characterization of such sheaves when the…
In this paper we construct new derived invariants with integral coefficients using the theory of motifs, and give several applications. Specifically, we obtain the following results: For complex algebraic surfaces, we prove that certain…
In this paper, we first prove a Donaldson-Uhlenbeck-Yau theorem over projective normal varieties smooth in codimension two. As a consequence we deduce the polystability of (dual) tensor products of stable reflexive sheaves, and we give a…
Cheeger-Simons differential characters and differential $K$-theory are refinements of ordinary cohomology theory and topological $K$-theory respectively, and they are examples of differential cohomology. Each of these differential…
Let $A$ be an excellent two-dimensional normal local ring containing an algebraically closed field and let $X\to \mathrm{Spec} (A)$ be a resolution of singularity. We prove a theorem giving a condition under which the dimension of the…
This work focuses on approximation and generation for the derived category of complexes with quasi-coherent cohomology on algebraic stacks. Our methods establish that approximation by compact objects descends along covers that are…
It was proved by Ginzburg and Mirkovic-Vilonen that the $G(O)$-equivariant perverse sheaves on the affine grassmannian of a connected reductive group $G$ form a tensor category equivalent to the tensor category of finite dimensional…