相关论文: Rickard's Derived Morita Theory: Review and Outloo…

We present a bicategorical perspective on derived Morita theory for rings, DG algebras, and spectra. This perspective draws a connection between Morita theory and the bicategorical Yoneda Lemma, yielding a conceptual unification of Morita…

By results of the second author, a source algebra equivalence between two $p$-blocks of finite groups induces an equivalence between the categories of cohomological Mackey functors associated with these blocks, and a splendid derived…

In this brief postscript to our paper "Integral transforms and Drinfeld centers in derived algebraic geometry", we describe a Morita equivalence for derived, categorified matrix algebras implied by theory developed since its appearance. We…

Derived equivalences and t-structures are closely related. We use realisation functors associated to t-structures in triangulated categories to establish a derived Morita theory for abelian categories with a projective generator or an…

For self-injective algebras, Rickard proved that each derived equivalence induces a stable equivalence of Morita type. For general algebras, it is unknown when a derived equivalence implies a stable equivalence of Morita type. In this…

This note uses a variation of graded Morita theory for finite dimensional superalgebras to determine explicitly the graded basic superalgebras for all real and complex Clifford superalgebras. As an application, the Grothendieck groups of…

Tilting theory has been a very important tool in the classification of finite dimensional algebras of finite and tame representation type, as well as, in many other branches of mathematics. Happel [Ha] proved that generalized tilting…

We prove two results from Morita theory of stable model categories. Both can be regarded as topological versions of recent algebraic theorems. One is on recollements of triangulated categories, which have been studied in the algebraic case…

Categorical equivalences between block algebras of finite groups - such as Morita and derived equivalences - are well-known to induce character bijections which commute with the Galois groups of field extensions. This is the motivation for…

In this paper, we characterize a Rickard complex, which induces a Rickard equivalence between the block algebras of a block $b$ and its Brauer correspondent and whose vertices have the same order as defect groups of the block $b$. The…

The Morita context provided by an exact module category over a finite tensor category gives a two-object bicategory with duals. Right and left duals of objects in the module category are given by internal Homs and coHoms, respectively. We…

This paper is a continuation and a completion of [BoRo1]. We extend the Jordan decomposition of blocks: we show that blocks of finite groups of Lie type in non-describing characteristic are Morita equivalent to blocks of subgroups…

We extend categorical Morita equivalence to finite tensor categories graded by a finite group $G$. We show that two such categories are graded Morita equivalent if and only if their equivariant Drinfeld centers are equivalent as braided…

Rickard proved that for certain self-injective algebras, a stable equivalence induced from an exact functor is a stable equivalence of Morita type, in the sense of Brou\'{e}. In this paper we study singular equivalences of finite…

In this note, I define a notion of a compactly supported object in a triangulated category. I prove a number of propositions relating this to traditional notions of support and give an application to the theory of derived Morita…

In this paper, we study ideal quotients of triangulated categories by higher cluster tilting subcategories. Koenig and Zhu proved that the ideal quotient by a $2$-cluster tilting subcategory is an abelian category; moreover, by Morita's…

This paper surveys some recent results, concerning the intrinsicness of natural subcategories of weakly approximable triangulated categories. We also review the results about uniqueness of enhancements of triangulated categories, with the…

In this paper we investigate equivariant Morita theory for algebras with momentum maps and compute the equivariant Picard groupoid in terms of the Picard groupoid explicitly. We consider three types of Morita theory: ring-theoretic…

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…

Two rings A and B are said to be derived Morita equivalent if their derived categories of modules are equivalent. By results of Rickard, if A and B are derived Morita equivalent algebras over a field k, then there is a complex of bimodules…