Related papers: Model category structures arising from Drinfeld ve…

For any admissible subcategory of the bounded derived category of coherent sheaves on a smooth proper variety, we prove that sections of the canonical bundle impose a strong constraint on the supports of the objects of the subcategory or…

Representations of vertex operator algebras define sheaves of coinvariants and conformal blocks on moduli of stable pointed curves. Assuming certain finiteness and semisimplicity conditions, we prove that such sheaves satisfy the…

The filter quotient construction is a particular instance of a filtered colimit of categories. It has primarily been considered in the context of categorical logic, where it has been used effectively to construct non-trivial models, for…

To a bicomplex one can associate two natural filtrations, the column and row filtrations, and then two associated spectral sequences. This can be generalized to $N$-multicomplexes. We present a family of model category structures on the…

The moduli spaces of stable sheaves on projective schemes admit certain gluing data of Kapranov's NC structures, which we call quasi NC structures. The formal completion of the quasi NC structure at a closed point coincides with the…

We prove that the bundles with flat connections on configuration spaces associated to braided fusion categories, as well as the bundles with flat connections on moduli spaces of curves (conformal blocks) associated to modular fusion…

In their article "Elementary construction of perverse sheaves", R.MacPherson and K. Vilonen show that on a Thom-Mather space X the category PervX of perverse sheaves is equivalent to the category C(F, G, T) whose objects are data of…

In these notes, an introduction to derived categories and derived functors is given. The main focus is the bounded derived category of coherent sheaves on a smooth projective variety.

The Corlette-Donaldson-Hitchin-Simpson's correspondence states that, on a compact K\"ahler manifold $(X, \omega )$, there is a one-to-one correspondence between the moduli space of semisimple flat complex vector bundles and the moduli space…

We propose a conjecture on the structure of the bounded derived category of coherent sheaves of the moduli space rank $2$ parabolic bundles on $\mathbb{P}^1$.

We show that conically smooth stratified spaces embed fully faithfully into $\infty$-categories. This articulates a stratified generalization of the homotopy hypothesis proposed by Grothendieck. As such, each $\infty$-category defines a…

Let $R$ be a ring with identity. Inspired by recent work of Emmanouil, we show that the derived category of $R$ is equivalent to the chain homotopy category of all K-flat complexes with pure-injective components. This is implicitly related…

Given a certain kind of linear representation of a reductive group, referred to as a quasi-symmetric representation in recent work of \v{S}penko and Van den Bergh, we construct equivalences between the derived categories of coherent sheaves…

In this paper, we construct new characteristic classes of fiber bundles via flat connections with values in infinite-dimensional Lie algberas of derivations. In fact, choosing a fiberwise metric, we construct a chain map to the de Rham…

A degree $d$ genus $g$ cover of the complex projective line by a smooth irreducible curve $C$ yields a vector bundle on the projective line by pushforward of the structure sheaf. We classify the bundles that arise this way when $d = 5$.…

In the paper "Cotorsion Pairs in C(R-Mod)", the authors construct an abelian model structure on the category of chain complexes Ch(R), where the class of cofibrant objects is given by the class of degreewise projective chain complexes.…

We study the following generalization of singularity categories. Let X be a quasi-projective Gorenstein scheme with isolated singularities and A a non-commutative resolution of singularities of X in the sense of Van den Bergh. We introduce…

In this paper we consider a construction in an arbitrary triangulated category T which resembles the notion of a Moore spectrum in algebraic topology. Namely, given a compact object C of T satisfying some finite tilting assumptions, we…

We develop a categorical approach to quivers and their modules. Naturally this leads to a notion of an action of a monoidal category on quivers. Using this, we construct for a large class of quivers rigid monoidal structures on their…

Representations of certain vertex algebras, here called of CohFT-type, can be used to construct vector bundles of coinvariants and conformal blocks on moduli spaces of stable curves [DGT2]. We show that such bundles define semisimple…