相关论文: Differential graded enhancements of singularity ca…

We consider recollements of derived categories of dg-algebras induced by self orthogonal compact objects obtaining a generalization of Rickard's Theorem. Specializing to the case of partial tilting modules over a ring, we extend the results…

A new homological dimension is introduced to measure the quality of resolutions of `singular' finite dimensional algebras (of infinite global dimension) by `regular' ones (of finite global dimension). Upper bounds are established in terms…

We investigate the relationship between differential graded algebras (dgas) and topological ring spectra. Every dga C gives rise to an Eilenberg-Mac Lane ring spectrum denoted HC. If HC and HD are weakly equivalent, then we say C and D are…

We study the singularities of the projective dual variety.

We show that the category of corings over a fixed base ring with local units is equivalent to the category of comonads in (right) unital modules whose underlying functors preserve inductive limits. Changing base rings, we prove a…

Differential graded (DG) algebras are powerful tools from rational homotopy theory. We survey some recent applications of these in the realm of homological commutative algebra.

The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.

This is the second in a series of papers laying the foundations for a differential graded approach to derived differential geometry (and other geometries in characteristic zero). In this paper, we extend the classical notion of a dg-algebra…

Magnitude is a numerical invariant of enriched categories, including in particular metric spaces as $[0,\infty)$-enriched categories. We show that in many cases magnitude can be categorified to a homology theory for enriched categories,…

In this article we develop formal category theory within augmented virtual double categories. Notably we formalise the classical notions of Kan extension, Yoneda embedding $\text y_A\colon A \to \hat A$, exact square, total category and…

The behaviour under coarsening functors of simple, entire, or reduced graded rings, of free graded modules over principal graded rings, of superfluous monomorphisms and of homological dimensions of graded modules, as well as adjoints of…

We construct a triangle equivalence between the singularity categories of two isolated cyclic quotient singularities of Krull dimensions two and three, respectively. This is the first example of a singular equivalence involving connected…

Reflexive dg categories were introduced by Kuznetsov and Shinder to abstract the duality between bounded and perfect derived categories. In particular this duality relates their Hochschild cohomologies, autoequivalence groups, and…

I show that the theories of enrichment in a monoidal infinity-category defined by Hinich and by Gepner-Haugseng agree, and that the identification is unique. Among other things, this makes the Yoneda lemma available in the former model.

This is an extended introduction to discrete valuation rings and Dedekind domains. Some natural generalizations of Dedekind domains are also (briefly) discussed including "almost Dedekind domains", Pr\"ufer domains, Krull domains, and…

We work over a perfect field. Recent work of the third-named author established a Derived Auslander Correspondence that relates finite-dimensional self-injective algebras that are twisted $3$-periodic to algebraic triangulated categories of…

Let $T=(A,M,0,B)$ be a triangular matrix algebra with its corner algebras $A$ and $B$ Artinian and $_AM_B$ an $A$-$B$-bimodule. The 2-recollement structures for singularity categories and Gorenstein defect categories over $T$ are studied.…

For a finite dimensional algebra $\Lambda$ of finite representation type and an additive generator $M$ for $\mathrm{mod}\,\Lambda$, we investigate the properties of the Yoneda algebra $\Gamma=\bigoplus_{i \geq…

We construct an "almost involution" assigning a new DG-category to a given one, and use this construction to recover, say, the abelian category of graded modules over the graded ring $R^*$ from the DG-category of DG-modules over a DG-ring…

We classify group gradings on the simple Lie algebra $L$ of type $D_4$ over an algebraically closed field of characteristic different from 2: fine gradings up to equivalence and $G$-gradings, with a fixed group $G$, up to isomorphism. For…