AbstractBuilding on the concept of a smooth DG algebra we define the notion of a smooth derived category. We then propose the definition of a categorical resolution of singularities. Our main example is the derived category D(X) of quasi-coherent sheaves on a scheme X. We prove that D(X) has a canonical categorical resolution if the base field is perfect and X is a separated scheme of finite type with a dualizing complex
We introduce perfect resolving algebras and study their fundamental properties. These algebras are b...
We define the notion of singular support of a coherent sheaf on a quasi-smooth-derived scheme or Art...
AbstractWe prove in this paper that for a quasi-compact and semi-separated (nonnecessarily noetheria...
AbstractBuilding on the concept of a smooth DG algebra we define the notion of a smooth derived cate...
We show that the derived category of any singularity over a field of characteristic 0 can be embedde...
We prove an equivalence between the derived category of a variety and the equivariant/ graded singul...
In this article we construct a categorical resolution of singularities of an excellent reduced curve...
This paper surveys the recent advances concerning the relations between triangulated (or derived) ca...
Categorical resolution of singularities has been constructed in [KL]. It proceeds by alternating two...
AbstractWe prove that the bounded derived category of coherent sheaves with proper support is equiva...
Derived algebraic geometry is a far-reaching generalization of algebraic geometry. It has found nume...
We prove that the derived category of a Grothendieck abelian category has a unique dg enhancement. U...
We introduce the notion of categorical absorption of singularities: an operation that removes from t...
Given a singular scheme X over a field k, we consider the problem of resolving the singularities of ...
In these notes, an introduction to derived categories and derived functors is given. The main focus ...
We introduce perfect resolving algebras and study their fundamental properties. These algebras are b...
We define the notion of singular support of a coherent sheaf on a quasi-smooth-derived scheme or Art...
AbstractWe prove in this paper that for a quasi-compact and semi-separated (nonnecessarily noetheria...
AbstractBuilding on the concept of a smooth DG algebra we define the notion of a smooth derived cate...
We show that the derived category of any singularity over a field of characteristic 0 can be embedde...
We prove an equivalence between the derived category of a variety and the equivariant/ graded singul...
In this article we construct a categorical resolution of singularities of an excellent reduced curve...
This paper surveys the recent advances concerning the relations between triangulated (or derived) ca...
Categorical resolution of singularities has been constructed in [KL]. It proceeds by alternating two...
AbstractWe prove that the bounded derived category of coherent sheaves with proper support is equiva...
Derived algebraic geometry is a far-reaching generalization of algebraic geometry. It has found nume...
We prove that the derived category of a Grothendieck abelian category has a unique dg enhancement. U...
We introduce the notion of categorical absorption of singularities: an operation that removes from t...
Given a singular scheme X over a field k, we consider the problem of resolving the singularities of ...
In these notes, an introduction to derived categories and derived functors is given. The main focus ...
We introduce perfect resolving algebras and study their fundamental properties. These algebras are b...
We define the notion of singular support of a coherent sheaf on a quasi-smooth-derived scheme or Art...
AbstractWe prove in this paper that for a quasi-compact and semi-separated (nonnecessarily noetheria...
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