Related papers: Relations between derived Hochschild functors via …

Let $\k$ be a commutative ring, and let $(A,\mfrak{a})$ be an adic ring which is a $\k$-algebra. We study complete and torsion versions of the derived Hochschild homology and cohomology functors of $A$ over $\k$. To do this, we first…

Grothendieck duality theory assigns to essentially-finite-type maps f of noetherian schemes a pseudofunctor f^\times right-adjoint to Rf_*, and a pseudofunctor f^! agreeing with f^\times when f is proper, but equal to the usual inverse…

Let $K$ be a Gorenstein noetherian ring of finite Krull dimension, and consider the category of cohomologically noetherian commutative differential graded rings $A$ over $K$, such that $H^0(A)$ is essentially of finite type over $K$, and…

We study functors underlying derived Hochschild cohomology, also called Shukla cohomology, of a commutative algebra S essentially of finite type and of finite flat dimension over a commutative noetherian ring K. We construct a complex of…

This paper classifies the derivations of twisted group algebras in terms of the generators and defining relations of the group. In particular, we generalize some know results over group algebras to the case of twisted group algebras. We…

The article primarily surveys work that followed from the formulas discovered by Avramov and Iyengar in 2008, which permit one to compute certain Hochschild homology and cohomology modules as expressions involving dualizing complexes. One…

This article is devoted to the investigation of the deformation (twisting) of monoidal structures, such as the associativity constraint of the monoidal category and the monoidal structure of monoidal functor. The sets of twistings have a…

We give in this paper an isomorphism theorem between derived functors over categories of modules.There is a nice class of categories that gives examples in which this theorem applies for a special construction. This leads us to a new…

For a recollement $(\mathcal{D}B,\mathcal{D}A,\mathcal{D}C)$ of derived categories of algebras, we investigate when the functor $j^*:\mathcal{D}A\rightarrow\mathcal{D}C$ is an eventually homological isomorphism. In this context, we compare…

We introduce Hochschild (co-)homology of morphisms of schemes or analytic spaces and study its fundamental properties. In analogy with the cotangent complex we introduce the so called (derived) Hochschild complex of a morphism; the…

Given a split $\mathbb{P}$-functor $F:\mathcal{D}^b(X) \to \mathcal{D}^b(Y)$ between smooth projective varieties, we provide necessary and sufficient conditions, in terms of the Hochschild cohomology of $X$, for it to become spherical on…

The notion of a duality between two derived functors as well as an extension theorem for derived functors to larger categories in which they need not be defined is introduced. These ideas are then applied to extend and study the coext…

Let A be a \C-algebra with an action of a finite group G, let $\natural$ be a 2-cocycle on $G$ and consider the twisted crossed product $A \rtimes \C [G,\natural]$. We determine the Hochschild homology of $A \rtimes \C [G,\natural]$ for two…

Twisted separable functors generalize the separable functors of Nastasescu, Van den Bergh and Van Oystaeyen, and provide a convenient tool to compare various projective dimensions. We discuss when an adjoint functor is twisted separable,…

In this paper we treat Grothendieck Duality for noetherian rings via rigid dualizing complexes. In particular, we prove that every ring, essentially finite type over a regular base ring, has a unique rigid dualizing complex. The rigid…

We define Hochschild cohomology of the second kind for differential graded (dg) or curved algebras as a derived functor in the twisted derived category, and show that it is invariant under suitable Morita equivalences of the second kind. A…

We study generalised Taylor morphisms, functors which construct differential ring homomorphisms from ring homomorphisms in a uniform way, analogous to the Taylor expansion for smooth functions. We generalise the construction of the twisted…

We define a class of morphisms between \'etale groupoids and show that there is a functor from the category with these morphisms to the category of $C^*$-algebras. We show that all homomorphisms between Cartan pairs of $C^*$-algebras that…

We generalize the adjunction between the functors $Rf_*$ and $f^!$ of derived categories of quasi-coherent sheaves for proper morphisms $f\colon X \to Y$ of Noetherian schemes to the following situation: Let $f$ be a finite type morphism…

Let $A$ be either a simplicial complex $K$ or a small category $\mathcal C$ with $V(A)$ as its set of vertices or objects. We define a twisted structure on $A$ with coefficients in a simplicial group $G$ as a function $$ \delta\colon…