相关论文: Deformations of overconvergent isocrystals on the …

Let H be a differential graded Hopf algebra over a field k. This paper gives an explicit construction of a triple cochain complex that defines the Hochschild-Cartier cohomology of H. A certain truncation of this complex is the appropriate…

Let X be a separated finite type scheme over a noetherian base ring K. There is a complex C(X) of topological O_X-modules on X, called the complete Hochschild chain complex of X. To any O_X-module M - not necessarily quasi-coherent - we…

Cohesive modules give a dg-enhancement of the bounded derived category of coherent sheaves on a complex manifold via superconnections. In this paper we discuss the deformation theory of cohesive modules on compact complex manifolds. This…

Let $\mathcal{V}$ be a mixed characteristic complete discrete valuation ring, $k$ its residual field, $\mathcal{P}$ a proper smooth formal scheme over $\mathcal{V}$, $P$ its special fiber, $T$ a divisor of $P$, $U:=P\setminus T$, $Y$ a…

We introduce the notion of integrable connections for a sheaf of differential graded algebras on a topological space. We then describe them in the finite locally projective setting, when the sheaf is either the de Rham complex of a formal…

We define the appropriate homological setting to study deformation theory of complete locally convex (curved) dg-algebras based on Positselski's contraderived categories. We define the corresponding Hochschild complex controlling…

First three sections of this overview paper cover classical topics of deformation theory of associative algebras and necessary background material. We then analyze algebraic structures of the Hochschild cohomology and describe the relation…

We study modules over stacks of deformation quantization algebroids on complex Poisson manifolds. We prove finiteness and duality theorems in the relative case and construct the Hochschild class of coherent modules. We prove that this class…

Given an associative unital algebra $A$ over a perfect field $k$ of odd positive characteristic, we construct a non-commutative generalization of the Cartier isomorphism for $A$. The role of differential forms is played by Hochschild…

This paper is the continuation of arXiv:0802.1245. We construct the Hochschild class for coherent modules over a deformation quantization algebroid on a complex Poisson manifold. We also define the convolution of Hochschild homologies, and…

Algebraic deformations of modules over a ring are considered. The resulting theory closely resembles Gerstenhaber's deformation theory of associative algebras.

We examine the Hochschild cohomology governing graded deformations for finite cyclic groups acting on polynomial rings. We classify the infinitesimal graded deformations of the skew group algebra $S\rtimes G$ for a cyclic group $G$ acting…

Let X be a an affine smooth symplectic variety over $\mathbb{Z}/p\mathbb{Z},$ and A be its deformation quantization over the p-adic integers. We prove that for all $n\geq 1,$ the Hochschild cohomogy of $A/p^nA$ is isomorphic to the de…

We investigate deformations of a skew group algebra that arise from a finite group acting on a polynomial ring. When the characteristic of the underlying field divides the order of the group, a new type of deformation emerges that does not…

We show for a coring which is finitely generated projective as a left module that the Cartier cohomology is isomorphic to the relative Hochschild cohomology of the right algebra. Furthermore, we show that this isomorphism lifts to the level…

Graph cocycles for star-products are investigated from the combinatorial point of view, using Connes-Kreimer renormalization techniques. The Hochschild complex, controlling the deformation theory of associative algebras, is the ``Kontsevich…

In present paper we develop the deformation theory of operads and algebras over operads. Free resolutions (constructed via Boardman-Vogt approach) are used in order to describe formal moduli spaces of deformations. We apply the general…

We show that the deformation theory of a perfect complex and that of its determinant are related by the trace map, in a general setting of sheaves on a site. The key technical step, in passing from the setting of modules over a ring where…

We introduce the notion of being cohomologically complete for objects of the derived category of sheaves of $Z[\hbar]$-modules on a topological space. Then we consider a $Z[\hbar]$-algebra satisfying some suitable conditions and prove…

We study the deformation theory of morphisms of properads and props thereby extending to a non-linear framework Quillen's deformation theory for commutative rings. The associated chain complex is endowed with a Lie algebra up to homotopy…