Related papers: Layers of the Coradical Filtration

We study the canonical Hodge filtration on the sheaf $\mathscr{O}_X(*D)$ of meromorphic functions along a divisor. For a germ of an analytic function $f$ whose Bernstein-Sato's polynomial's roots are contained in $(-2,0)$, we: give a simple…

We compute the Hodge filtration on cohomology groups of complements of complex coordinate subspace arrangements. By means of this result we construct integral representations of holomorphic functions such that kernels of these…

We prove that many of the recently-constructed algebras and categories which appear in categorification can be equipped with an action of $\mathfrak{sl}_2$ by derivations. The $\mathfrak{sl}_2$ representations which appear are filtered by…

We determine the Hall algebra, in the sense of Toen, of the algebraic triangulated category generated by a spherical object.

We introduce an algebraic method for describing the Hodge filtration of degenerating hypersurfaces in projective toric varieties. For this purpose, we show some fundamental properties of logarithmic differential forms on proper equivariant…

We give explicit formulas for the Hodge filtration on mixed Hodge modules associated with certain hypersurfaces.

We show that one can use model categories to construct rational orthogonal calculus. That is, given a continuous functor from vector spaces to based spaces one can construct a tower of approximations to this functor depending only on the…

We recall the notions of a graded cocategory, conilpotent cocategory, morphisms of such (cofunctors), coderivations and define their analogs in $\mathbb L$-filtered setting. The difference with the existing approaches: we do not impose any…

We show that the category of comodules over a coassociative coalgebra in a complete, cocomplete and well-powered category has limits and colimits under additional assumptions.

We compute the the Balmer spectra of compact objects of tensor triangulated categories whose objects are filtered or graded objects of (or sheaves valued in) another tensor triangulated category. Notable examples include the filtered…

Coalgebras for an endofunctor provide a category-theoretic framework for modeling a wide range of state-based systems of various types. We provide an iterative construction of the reachable part of a given pointed coalgebra that is inspired…

We define a filtration indexed by the integers on the tensor product of an integrable highest weight module and a loop module for a quantum affine algebra. We prove that the filtration is either trivial or strictly decreasing and give…

We interpret tensors on a smooth manifold M as differential forms over a graded commutative algebra called the algebra of iterated differential forms over M. This allows us to put standard tensor calculus in a new differentially closed…

We describe categories of equivariant vector bundles on certain toroidal spherical varieties in linear algebra terms: vector spaces equipped with filtrations, group and Lie algebra actions, and linear maps preserving these structures.

Earlier the authors considered and, in some cases, computed Poincare series of two sorts of multi-index filtrations on the ring of germs of functions on a complex (normal) surface singularity (in particular on the complex plane). A…

We introduce the concept of cotensor coalgebra for a given bicomodule over a coalgebra in an abelian monoidal category. Under some further conditions we show that such a cotensor coalgebra exists and satisfies a meaningful universal…

Let ${\mathcal F}_\lambda(\mathbb{S}^n)$ be the space of tensor densities on $\mathbb{S}^n$ of degree $\lambda$. We consider this space as an induced module of the nonunitary spherical series of the group $\mathrm{SO}_0(n+1,1)$ and classify…

Given an irreducible well-generated complex reflection group, we construct an explicit basis for the module of vector fields with logarithmic poles along its reflection arrangement. This construction yields in particular a Hodge filtration…

We consider the Hodge filtration on the sheaf of meromorphic functions along free divisors for which the logarithmic comparison theorem holds. We describe the Hodge filtration steps as submodules of the order filtration on a cyclic…

We prove a conjecture stated in a previous paper by the author about the existence of canonical filtrations for a family of vertex operator algebras in rational levels.