Related papers: Local dualisable objects in local algebra
In three recaent papers of G. Dimov, many Stone-type duality theorems for the category of locally compact Hausdorff spaces and continuous maps and some of its subcategories were proved. The dual objects in all these theorems are the local…
The present paper presents a survey of some recent results devoted to derivations, local derivations and 2-local derivations on various algebras of measurable operators affiliated with von Neumann algebras. We give a complete description of…
We introduce a concept of formal local homology modules which is in some sense dual to P. Schenzel's concept of formal local cohomology modules. The dual theorem and the non-vanishing theorem of formal local homology modules will be shown.…
We generalize the concepts of locally presentable and accessible categories. Our framework includes such categories as small presheaves over large categories and ind-categories. This generalization is intended for applications in the…
We develop the notions of multiplicative Lie conformal and Poisson vertex algebras, local and non-local, and their connections to the theory of integrable differential-difference Hamiltonian equations. We establish relations of these…
This paper establishes a second vanishing theorem for formal local cohomology modules over Noetherian local rings. We introduce the \textit{formal dimension} invariant and characterize the vanishing of higher formal local cohomology in…
The work is my Ph D thesis (dissertation for obtaining candidate of sciences degree in Russia) fulfilled under direction of D. A. Raikov and defended under supervision of N. Ya. Vilenkin and S. V. Ptchelintsev. In the dissertatin I gave…
We prove a categorical duality between a class of abstract algebras of partial functions and a class of (small) topological categories. The algebras are the isomorphs of collections of partial functions closed under the operations of…
This paper generalizes the normally ordered tensor product from Tate vector spaces to Tate objects over arbitrary exact categories. We show how to lift bi-right exact monoidal structures, duality functors, and construct external Homs. We…
A duality theorem for the category of locally compact Hausdorff spaces and continuous maps which generalizes the well-known Duality Theorem of de Vries is proved.
We show that a $\mathbb{P}$-object and simple configurations of $\mathbb{P}$-objects have a formal derived endomorphism algebra. Hence the triangulated category (classically) generated by such objects is independent of the ambient…
It is known that the category of Lie algebras over a ring admits algebraic exponents. The aim of this paper is to show that the same is true for the category of internal Lie algebras in an additive, cocomplete, symmetric, closed, monoidal…
We consider Lie algebroids over an algebraic space (or topological ringed space) as quasicoherent sheaves of Lie-Rinehart algebras. We express hypercohomology for a locally free Lie algebroid (not necessarily of finite rank) as a derived…
Two left noetherian rings $R$ and $S$ are said to be {\it singularly equivalent} if their singularity categories are equivalent as triangulated categories. The aim of this paper is to give a necessary condition for two commutative…
We propose a new framework for the study of homological properties for (compactly generated) triangulated categories such as regularity, finiteness of global or finitistic dimension, gorensteinness or injective generation and the relation…
We propose a new look on triangulated categories, which is based on the second Hochschild cohomology.
We investigate the triangulated hull of the orbit categories of the perfect derived category and the bounded derived category of a ring concerning the power of the suspension functor. It turns out that the triangulated hull will correspond…
We show for a ring R of weak global dimension at most one that there is a bijection between the smashing subcategories of its derived category and the equivalence classes of homological epimorphisms starting in R. If, moreover, R is…
We present methods and explicit formulas for describing simple weight modules over twisted generalized Weyl algebras. When a certain commutative subalgebra is finitely generated over an algebraically closed field we obtain a classification…
This work presents an exposition of both the internal structure of derived category of an abelian category D*(A) and its contribution in solving problems, particularly in algebraic geometry. Calculation of some morphisms will be presented…