Related papers: Localization of Atiyah classes
Local cohomology techniques in equivariant homotopy theory, introduced by John Greenlees, may be applied to understand homology of classifying spaces through other equivariant data. In this paper we relate the local cohomology filtration to…
For g>2 we study the cohomology classes in the closure of a stratum of abelian differentials defined by the boundary strata of codimension one. As an application, we find an explicit stratification of the spin moduli space for an odd spin…
The main purpose of this paper is to provide a full cohomology of a Hom-pre-Lie algebra with coefficients in a given representation. This new type of cohomology exploit strongly the Hom-type structure and fits perfectly with simultaneous…
The purpose of this paper is to study global deformations of Hom-Leibniz algebras. We introduce a cohomology for Hom-Leibniz algebras with values in a Hom-module, characterize versal deformations and provide examples.
In this paper, first we show that under the assumption of the center of h being zero, diagonal non-abelian extensions of a regular Hom-Lie algebra g by a regular Hom-Lie algebra h are in one-to-one correspondence with Hom-Lie algebra…
In this article we study cohomology of a group with coefficients in representations on Banach spaces and its stability under deformations. We show that small, metric deformations of the representation preserve vanishing of cohomology. As…
Deformation quantization on varieties with singularities offers perspectives that are not found on manifolds. Essential deformations are classified by the Harrison component of Hochschild cohomology, that vanishes on smooth manifolds and…
The aim of this paper is to extend Gerstenhaber formal deformations of algebras to the case of Hom-Alternative and Hom-Malcev algebras. We construct deformation cohomology groups in low dimensions. Using a composition construction, we give…
The theory of unified product and extending structures for alternative and pre-alternative algebras are developed. It is proved that the extending structures of these algebras can be classified by using some non-abelian cohomology and…
We develop the deformation-obstruction calculus for morphisms of complexes with a fixed lift of the codomain, to derived categories of flat nilpotent deformations of abelian categories. As an application, we give an alternative proof that…
Starting from simple and necessary axioms on a (derivator enhanced) four-functor-formalism, we construct derivator six-functor-formalisms using compactifications. This works, for instance, for the stable homotopy categories of…
This article investigates the relationship between Betti numbers of finitely generated modules over a Noetherian local ring $(R, \mathfrak{m})$ and the structure of formal local cohomology modules. We establish a connection between the…
In this paper, we review how local potentials arise in the Wu-Yang topological quantization. We also discuss the isomorphism between the de Rham cohomology classes and Cech cohomology classes in such topological quantization. We also…
This paper is a companion of the paper "Weil's conjecture for function fields" by J. Lurie and the author. We present a different exposition of essentially the same algebro-geometric proof of the Atiyah-Bott for the cohomology of Bun(G),…
In this paper, we first recall the notion of (noncommutative) Poisson conformal algebras and describe some constructions of them. Then we study the formal distribution (noncommutative) Poisson algebras and coefficient (noncommutative)…
Due to the immense importance of BiHom Type algebras and cohomology of various algebraic structures, this paper is devoted to defining the BiHom-associative dialgebra, its derivation, generalized derivation, and quasi-derivation. We…
In this paper, we introduce the concepts of representation and dual representation for averaging Leibniz algebras. We also develop a cohomology theory for these algebras. Additionally, we explore the infinitesimal and formal deformation…
This paper at first concerns some criteria on Artinianness and vanishing of formal local cohomology modules. Then we consider the cosupport and the set of coassociated primes of these modules more precisely.
As an algebraic study of differential equations, differential algebras have been studied for a century and and become an important area of mathematics. In recent years the area has been expended to the noncommutative associative and Lie…
In this paper, we develop a cohomology theory of a left-symmetric conformal algebra and study its some applications. We define the cohomology of a left-symmetric conformal algebra, and then give an isomorphism between the cohomology spaces…