Related papers: Fukaya categories in Koszul duality theory
We begin with proving a formula relating the Hilbert series of a graded algebra $A$ and the Poincar\'{e} series for $A$ in two variables. This gives the Fr\"oberg formula in the case where the bigraded $Tor^A(k,k)$ is concentrated on the…
In this article we construct various models for singularity categories of modules over differential graded rings. The main technique is the connection between abelian model structures, cotorsion pairs and deconstructible classes, and our…
We propose an analogue of the bounded derived category for an augmented ring spectrum, defined in terms of a notion of Noether normalization. In many cases we show this category is independent of the chosen normalization. Based on this, we…
We consider moduli spaces of Azumaya algebras on K3 surfaces and construct an example. In some cases we show a derived equivalence which corresponds to a derived equivalence between twisted sheaves. We prove if $A$ and $A'$ are Morita…
Given a closed, connected, relatively-spin Lagrangian submanifold in a closed symplectic manifold, we associate to it a curved, gapped, filtered, $A_{n, K}$-algebra over the Novikov ring with integer coefficients. Under certain conditions,…
Let R be a commutative noetherian ring. Let M be a finitely generated R-module. In this paper, we reconstruct M from its Koszul homology with respect to a suitable sequence of elements of R by taking direct summands, syzygies and…
A cubical Feynman category, introduced by the authors in previous work, is a category whose functors to a base category $\mathcal{C}$ behave like operads in $\mathcal{C}$. In this note we show that every cubical Feynman category is Koszul.…
Koszul duality and covering theory are combined to realise the bounded derived category D of an algebra with radical square zero as a certain orbit category of the bounded derived category of finitely presented representations of an…
We construct a version of Fourier transform for families of real tori. This transform defines a functor from certain category associated with a symplectic family of tori to the category of holomorphic vector bundles on the dual family (the…
The connective ku-(co)homology of elementary abelian 2-groups is determined as a functor of the elementary abelian 2-group. The argument requires only the calculation of the rank one case and the Atiyah-Segal theorem for KU-cohomology…
We establish equalities between cochain and chain type levels of maps by making use of exact functors which connect appropriate derived and coderived categories. Relevant conditions for levels of maps to be finite are extracted from the…
In this paper we construct a family of exact functors from the category of Whittaker modules of the simple complex Lie algebra of type $A_n$ to the category of finite-dimensional modules of the graded affine Hecke algebra of type $A_\ell$.…
We construct a monoidal model structure on the category of all curved coalgebras and show that it is Quillen equivalent, via the extended bar-cobar adjunction, to another model structure we construct on the category of curved algebras. When…
This paper is a companion to the authors' forthcoming work extending Heegaard Floer theory from closed 3-manifolds to compact 3-manifolds with two boundary components via quilted Floer cohomology. We describe the first interesting case of…
We establish a character formula for indecomposable tilting modules for connected reductive groups in characteristic p in terms of p-Kazhdan-Lusztig polynomials, for p>h the Coxeter number. Using results of Andersen, one may deduce a…
Differential categories were introduced by Blute, Cockett, and Seely as categorical models of differential linear logic and have since lead to abstract formulations of many notions involving differentiation such as the directional…
In this article we introduce the notion of \emph{multi-Koszul algebra} for the case of a nonnegatively graded connected algebra with a finite number of generators of degree 1 and with a finite number of relations, as a generalization of the…
We give a description of a certain induced module for a quantum group of type $A$. Together with our previous results this gives a proof of Lusztig's conjectural multiplicity formula for non-restricted modules over the De Concini-Kac type…
We develop Tannaka duality theory for dg categories. To any dg functor from a dg category $\mathcal{A}$ to finite-dimensional complexes, we associate a dg coalgebra $C$ via a Hochschild homology construction. When the dg functor is…
Generalising Jacob Lurie's idea on the relation between the Verdier duality and the iterated loop space theory, we study the Koszul duality for locally constant factorisation algebras. We formulate an analogue of Lurie's "nonabelian…