Moderate and formal cohomology associated with constructible sheaves
Moduli of objects in dg-categories
-angulated quotient categories induced by mutation pairs
Geiss, Keller and Oppermann (2013) introduced the notion of -angulated category, which is a “higher dimensional” analogue of triangulated category, and showed that certain -cluster tilting subcategories of triangulated categories give rise to -angulated categories. We define mutation pairs in -angulated categories and prove that given such a mutation pair, the corresponding quotient category carries a natural -angulated structure. This result generalizes a theorem of Iyama-Yoshino (2008) for...
Noncommutative localisation in algebraic -theory. I.
Obstructions for deformations of complexes
We develop two approaches to obstruction theory for deformations of derived isomorphism classes of complexes of modules for a profinite group over a complete local Noetherian ring of positive residue characteristic.
Octahedra and braids
On a certain generalization of spherical twists
This note gives a generalization of spherical twists, and describe the autoequivalences associated to certain non-spherical objects. Typically these are obtained by deforming the structure sheaves of -curves on threefolds, or deforming -objects introduced by D.Huybrechts and R.Thomas.
On derived categories and derived functors.
On derived equivalence classification of gentle two-cycle algebras
We classify, up to derived (equivalently, tilting-cotilting) equivalence, all nondegenerate gentle two-cycle algebras. We also give a partial classification and formulate a conjecture in the degenerate case.
On Neeman's well generated triangulated categories.
On nonstandard tame selfinjective algebras having only periodic modules
We investigate degenerations and derived equivalences of tame selfinjective algebras having no simply connected Galois coverings but the stable Auslander-Reiten quiver consisting only of tubes, discovered recently in [4].
On quasitilted algebras which are one-point extensions of hereditary algebras
Quasitilted algebras have been introduced as a proper generalization of tilted algebras. In an earlier article we determined necessary conditions for one-point extensions of decomposable finite-dimensional hereditary algebras to be quasitilted and not tilted. In this article we study algebras satisfying these necessary conditions in order to investigate to what extent the conditions are sufficient.
On the cyclic homology of ringed spaces and schemes.
On the derived categories of coherent sheaves on some homogeneous spaces.
On the derived category of a finite-dimensional algebra.
On the derived category of sheaves on a manifold.
On the Freyd categories of an additive category.
On the relation between maximal rigid objects and τ-tilting modules
This note compares τ-tilting modules and maximal rigid objects in the context of 2-Calabi-Yau triangulated categories. Let be a 2-Calabi-Yau triangulated category with suspension functor S. Let R be a maximal rigid object in and let Γ be the endomorphism algebra of R. Let F be the functor . We prove that any τ-tilting module over Γ lifts uniquely to a maximal rigid object in via F, and in turn, that projection from to mod Γ sends the maximal rigid objects which have no direct summands from add...
On the structure of Calabi-Yau categories with a cluster tilting subcategory.
On the structure of triangulated categories with finitely many indecomposables
We study the problem of classifying triangulated categories with finite-dimensional morphism spaces and finitely many indecomposables over an algebraically closed field . We obtain a new proof of the following result due to Xiao and Zhu: the Auslander-Reiten quiver of such a category is of the form where is a disjoint union of simply-laced Dynkin diagrams and a weakly admissible group of automorphisms of . Then we prove that for ‘most’ groups , the category is standard,i.e.-linearly...