Related papers: On D-modules of categories I

A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class--a…

Modular functors, i.e. consistent systems of projective representations of mapping class groups of surfaces, have been constructed for non-semisimple modular categories already decades ago. Concepts from homological algebra have not been…

The so called theory of derived D-modules is an extension of classical D-modules to derived algebraic geometry, which uses the derived information of the base scheme. We prove that the three different definitions of derived D-modules, given…

To any dg-category $T$ (over some base ring $k$), we define a $D^{-}$-stack $\mathcal{M}_{T}$ in the sense of \cite{hagII}, classifying certain $T^{op}$-dg-modules. When $T$ is saturated, $\mathcal{M}_{T}$ classifies compact objects in the…

We study the category of discrete modules over the ring of degree zero stable operations in p-local complex K-theory. We show that the p-local K-homology of any space or spectrum is such a module, and that this category is isomorphic to a…

We construct a diagrammatic categorification of the spherical module over the Hecke algebra. We establish a basis for the morphism spaces of this category, and prove that it is equivalent to an existing algebraic spherical category.

Pursuing a generalization of group symmetries of modular categories to category symmetries in topological phases of matter, we study linear Hopf monads. The main goal is a generalization of extension and gauging group symmetries to category…

For a projective variety V in P^n over a field of characteristic zero, with homogeneous ideal I in A = k[x0,x1,...,xn], we consider the local cohomology modules H^i_I(A). These have a structure of holonomic D-module over A, and we…

Let $k$ be an algebraically closed field of characteristic $p\ge 0$. Let $G$ be an affine group scheme over $k$. We classify the indecomposable exact module categories over the rigid tensor category $\text{Coh}_f(G)$ of coherent sheaves of…

We compute the rational homology of the moduli stack $\mathcal{M}$ of objects in the derived category of certain smooth complex projective varieties $X$ including toric varieties, flag varieties, curves, surfaces, and some 3- and 4-folds.…

Any finite-dimensional Hopf algebra H is Frobenius and the stable category of H-modules is triangulated monoidal. To H-comodule algebras we assign triangulated module-categories over the stable category of H-modules. These module-categories…

This paper solves the global moduli problem for regular holonomic D-modules with normal crossing singularities on a nonsingular complex projective variety. This is done by introducing a level structure (which gives rise to…

Let $ G $ be a cyclic group, in this paper, we study the Herbrand quotient and $ 1-$th cohomology group on finitely generated $ G-$modules in some cases. When $ G $ is of order $ 2, $ the order of the cohomology group is explicitly related…

Let $X$ be a smooth projective curve of genus $g\geq 2$ over the complex numbers. Fix $n\geq 2$, and an integer $d$. A pair $(E,\phi)$ over $X$ consists of an algebraic vector bundle $E$ of rank $n$ and degree $d$ over $X$ and a section…

Let $V$ be a complete discrete valuation ring with residue field $\mathbb{F}$. We define a cyclic homology theory for algebras over $\mathbb{F}$, by lifting them to free algebras over $V$, which we enlarge to tube algebras and complete…

Let H be a coFrobenius Hopf algebra over a field k. Let A be a right H-comodule algebra over k. We recall that the category of right H-comodules admits a certain model structure whose homotopy category is equivalent to the stable category…

Using a representation theoretic parameterization for the orbits in the enhanced cyclic nilpotent cone, derived by the authors in a previous article, we compute the fundamental group of these orbits. This computation has several…

In this survey, we first present basic facts on A-infinity algebras and modules including their use in describing triangulated categories. Then we describe the Quillen model approach to A-infinity structures following K. Lefevre's thesis.…

We construct a fully-faithful functor of $\infty$-categories from complexes of D-cap modules with Fr\'echet cohomology to quasi-coherent sheaves on an analytic stack. We prove various descent results for $\infty$-categories of D-cap modules…

We show that Higher Hochschild complex associated to a connected pointed simplicial set commutes with localization of commutative algebras over a field of characteristic zero. Then, we define in two ways higher order Hochschild cohomology…