Related papers: A descent criterion for equivalences between equiv…

In a perfect category every object has a minimal projective resolution. We give a criterion for the category of modules over a categorygraded algebra to be perfect.

We investigate a version of the Green correspondence for categories of complexes, including homotopy categories and derived categories. The correspondence is an equivalence between a category defined over a finite group $G$ and the same for…

We give a necessary and sufficient condition for a morphism between recollements of abelian categories to be an equivalence.

We provide a far reaching derived equivalence classification of the cluster-tilted algebras of Dynkin type D and suggest standard forms for the derived equivalence classes. We believe that the classification is complete, but some subtle…

In this expository note, we discuss some results of the author on the structure of derived categories of equivariant coherent sheaves and the derived categories of geometric invariant theory quotients. We take a recent perspective,…

This paper is devoted to the comparison of different localized categories of differential complexes. The first result is that the canonical functor from the category of complexes of differential operators of order one (defined by Herrera…

For a Serre subcategory $\mathscr L$ and a resolving subcategory $\mathscr A$ of an abelian category, we show that the derived equivalence $D^b(\overline{\mathscr A} \cap \mathscr L) \simeq D^b_{\mathscr L}(\mathscr A)$ holds under certain…

For a noetherian scheme, we introduce its unbounded stable derived category. This leads to a recollement which reflects the passage from the bounded derived category of coherent sheaves to the quotient modulo the subcategory of perfect…

We investigate under which assumptions a subclass of flat quasi-coherent shea\-ves on a quasi-compact and semi-separated scheme allows to "mock" the homotopy category of projective modules. Our methods are based on module theoretic…

We extend some recent results about bounded invariant equivalence relations and invariant subgroups of definable groups: we show that type-definability and smoothness are equivalent conditions in a wider class of relations than heretofore…

In these notes, an introduction to derived categories and derived functors is given. The main focus is the bounded derived category of coherent sheaves on a smooth projective variety.

We prove that the bounded derived category of coherent sheaves with proper support is equivalent to the category of locally-finite, cohomological functors on the perfect derived category of a quasi-projective scheme over a field. We…

We assume given a smooth symplectic (in the algebraic sense) resolution $X$ of an affine algebraic variety $Y$, and we prove that, possibly after replacing $Y$ with an etale neighborhood of a point, the derived category of coherent sheaves…

In this paper we give smoothness criterions for a good quotient Y of a smooth variety X by a reductive group G. Our results partially answer a question raised by J. Fogarty in the case where G is a finite group. They also give a converse to…

We describe the group of exact autoequivalences of the bounded derived category of coherent sheaves on a bielliptic surface. We achieve this by studying its action on the numerical Grothendieck group of the surface.

We study the equivalences induced by some special silting objects in the derived category over dg-algebra whose positive cohomologies are all zero.

This paper introduces two Gaussian graphical models defined on complete bipartite graphs. We show that the determinants of the precision matrices associated with the models are equal up to scale, where the scale factor only depends on model…

We study the class of equimultiple modules. In particular, we prove several criteria for an equimultiple module to be a complete intersection and prove the openness of the equimultiple locus of an ideal module.

For an abelian category, a category equivalent to its derived category is constructed by means of specific projective (injective) multicomplexes, the so-called homological resolutions.

In this paper we introduce a new approach for organizing algebras of global dimension at most 2. We introduce the notion of cluster equivalence for these algebras, based on whether their generalized cluster categories are equivalent. We are…