Related papers: Blockwise relations between triples, and derived e…
The Alperin--McKay conjecture relates irreducible characters of a block of an arbitrary finite group to those of its $p$-local subgroups. A refinement of this conjecture was stated by the author in a previous paper. We prove that this…
In this paper we study derived equivalences between triangular matrix algebras using certain classical recollements. We show that special properties of these recollements actually characterize triangular matrix algebras, and describe…
We give a characterization of the sets of objects of the derived category of a block of a finite group algebra (or other symmetric algebra) that occur as the set of images of simple modules under an equivalence of derived categories. We…
We give a new approach to the construction of derived equivalences between blocks of finite groups, based on perverse equivalences, in the setting of Brou\'e's conjecture. We provide in particular local and global perversity data describing…
In this article, a new construction of derived equivalences is given. It relates different endomorphism rings and more generally cohomological endomorphism rings - including higher extensions - of objects in triangulated categories. These…
We develop a new algebraic framework to reason about languages of Mazurkiewicz traces. This framework supports true concurrency and provides a non-trivial generalization of the wreath product operation to the trace setting. A novel local…
In this paper, we study homological dimensions of algebras linked by recollements of derived module categories, and establish a series of new upper bounds and relationships among their finitistic or global dimensions. This is closely…
We give an equivalence of triangulated categories between the derived category of finitely generated representations of symplectic reflection algebras associated with wreath products (with parameter t=0) and the derived category of coherent…
We prove a group graded Morita equivalences version of the "butterfly theorem" on character triples. This gives a method to construct an equivalence between block extensions from another related equivalence.
The article is concerned with the Foulkes characters of wreath products, which are block characters of wreath products, i.e., the positive-definite class functions depending only on the length of its elements. Inspired by the works of…
We establish a theory of complexes of relative correspondences. The theory generalizes the known theory of complexes of correspondences of smooth projective varieties. It will be applied in the sequel of this paper to the construction of…
We associate a t-structure to a family of objects in D(A), the derived category of a Grothendieck category A. Using general results on t-structures, we give a new proof of Rickard's theorem on equivalence of bounded derived categories of…
In this paper, we construct derived equivalences between matrix subrings. As applications, we calculate the global dimensions and the finitistic dimensions of some matrix subrings. And we show that the finitistic dimension conjecture holds…
We discuss relations between the motives of two varieties with equivalent derived categories of coherent sheaves.
Comparing the bounded derived categories of an algebra and of the endomorphism algebra of a given support {\tau}-tilting module, we find a relation between the derived dimensions of an algebra and of the endomorphism algebra of a given…
We introduce a new method for ``twisting'' relative equivalences of derived categories of sheaves on two spaces over the same base. The first aspect of this is that the derived categories of sheaves on the spaces are twisted. They become…
Mark Haiman has reduced Macdonald positivity conjecture to a statement about geometry of the Hilbert scheme of points on the plane, and formulated a generalization of the conjectures where the symmetric group is replaced by the wreath…
We introduce Morita and Rickard equivalences over a group graded G-algebra between block extensions. A consequence of such equivalences is that Sp\"ath's central order relation holds between two corresponding character triples.
Recollements of triangulated categories may be seen as exact sequences of such categories. Iterated recollements of triangulated categories are analogues of geometric or topological stratifications and of composition series of algebraic…
Le but cette note est de tenter d'expliquer les liens \'etroits qui unissent la th\'eorie des empilements de cercles et des modules combinatoires, et de comparer les approches \`a la conjecture de J.W. Cannon qui en d\'ecoulent. ???? The…