Related papers: On Koszul complex of a supermodule

We study the structure of mod 2 cohomology rings of oriented Grassmannians $\tilde{\operatorname{Gr}}_k(n)$ of oriented $k$-planes in $\mathbb{R}^n$. Our main focus is on the structure of the cohomology ring ${\rm…

Several spectral sequence techniques are used in order to derive information about the structure of finite free resolutions of graded modules. These results cover estimates of the minimal number of generators of defining ideals of…

This book contains a detailed exposition of the nonhomogeneous Koszul duality theory in the relative situation over a noncentral, noncommutative, nonsemisimple base ring, as announced in Section 0.4 of arXiv:0708.3398. We prove the…

We provide an algorithmic method for constructing projective resolutions of modules over quotients of path algebras. This algorithm is modified to construct minimal projective resolutions of linear modules over Koszul algebras.

We establish a twisted version of Skoda's estimate for the Koszul complex from which we get division theorems for the Koszul complex. This generalizes Skoda's division theorem. We also show how to use Skoda triples to produce division…

Let $G$ be a semisimple group, split over a non-Archimedean field $F$. We prove that the category of modules over the extension algebra of generalised Steinberg representations of $G(F)$ is equivalent to a full subcategory of equivariant…

This is a survey on recent progress in algebraic deformation theory and the application of algebraic operads to its study. We review the classical homotopical tools in the theory of algebraic operads, namely Koszul duality. We give concrete…

We study the differential graded Lie algebra of endomorphisms of the Koszul resolution of a regular sequence on a unitary commutative $K$-algebra $R$ and we prove that it is homotopy abelian over $K$, while it is generally not formal over…

We discuss recent progress on syzygies of curves, including proofs of Green's and Gonality Conjectures as well as applications of Koszul cycles to the study of the birational geometry of various moduli spaces of curves. We prove a number of…

Koszul and homogeneous Koszul algebras were defined by Priddy in \cite{Priddy1970}. There exist some relations between these algebras and the skew PBW extensions introduced in \cite{LezamaGallego}. In this paper we give conditions to…

This paper is a coalgebra version of arXiv:1703.04266 and a sequel to arXiv:1607.03066. We present the definition of a pseudo-dualizing complex of bicomodules over a pair of coassociative coalgebras $\mathcal C$ and $\mathcal D$. For any…

This paper provides an extensive study of the homotopy theory of types of algebras with units, like unital associative algebras or unital commutative algebras for instance. To this purpose, we endow the Koszul dual category of curved…

We study some spectral sequences associated with a locally free $\mathcal O_X$-module $\mathcal A$ which has a Lie algebroid structure. Here $X$ is either a complex manifold or a regular scheme over an algebraically closed field $k$. One…

This paper is the first in a series. The main goal of the series is to present a geometric construction of certain remarkable tensor categories arising from quantum groups coresponding to the value of deformation parameter $q$ equal to a…

We find the complex structure on the dual of a complex target space. For $N=(2,2)$ systems, we prove that the space orthogonal to the kernel of the commutator of the left and right complex structures is {\em always} integrable, and hence…

The notion of prop models the operations with multiple inputs and multiple outpus, acting on some algebraic structures like the bialgebras or the Lie bialgebras. In this paper, we generalize the Koszul duality theory of associative algebras…

In this work we classify the thick subcategories of the bounded derived category of dg modules over a Koszul complex on any list of elements in a regular ring. This simultaneously recovers a theorem of Stevenson when the list of elements is…

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…

In this paper, we attempt to determine the quantum cohomology of projective bundles over the projective space P^n. In contrast to the previous examples, the relevant moduli spaces in our case frequently do not have expected dimensions. It…

We extend the theory of Koszul and Buchsbaum-Eisenbud complexes to modules over commutative OI-algebras and show that they still have the familiar properties of the classical complexes. In particular, the OI-complexes are generically…