## 48 Citations

### On the uniqueness of infinity-categorical enhancements of triangulated categories.

- Mathematics
- 2018

We study the problem of when triangulated categories admit unique infinity-categorical enhancements. Our results use Lurie's theory of prestable infinity-categories to give conceptual proofs of, and…

### Uniqueness of enhancements for derived and geometric categories

- Mathematics
- 2021

We prove that the derived categories of abelian categories have unique enhancements— all of them, the unbounded, bounded, bounded above and bounded below derived categories. The unseparated and left…

### Equivariant derived categories

- MathematicsMathematical Surveys and Monographs
- 2021

We study the equivariant category associated to a finite group action on the derived category of coherent sheaves of a smooth projective variety. We discuss decompositions of the equivariant category…

### An example of a non-Fourier–Mukai functor between derived categories of coherent sheaves

- MathematicsInventiones mathematicae
- 2019

Orlov’s famous representability theorem asserts that any fully faithful exact functor between the bounded derived categories of coherent sheaves on smooth projective varieties is a Fourier–Mukai…

### Derived categories of hearts on Kuznetsov components

- Mathematics
- 2022

We prove a general criterion which guarantees that an admissible subcategory K of the derived category of an abelian category is equivalent to the bounded derived category of the heart of a bounded…

### Derived Categories

- Mathematics
- 2019

This is the fourth (and last) prepublication version of a book on derived categories, that will be published by Cambridge University Press. The purpose of the book is to provide solid foundations for…

### Liftable derived equivalences and objective categories

- MathematicsBulletin of the London Mathematical Society
- 2020

We give two proofs of the following theorem and a partial generalization: if a finite‐dimensional algebra A is derived equivalent to a smooth projective scheme, then any derived equivalence between A…

### Formality and strongly unique enhancements

- Mathematics
- 2022

Inspired by the intrinsic formality of graded algebras, we prove a necessary and sufﬁcient condition for strongly uniqueness of DG-enhancements. This approach offers a generalization to linearity…

### Notes on equivariant categories

- Mathematics
- 2020

We give a mostly self-contained introduction to equivariant categories with a focus on the derived category of coherent sheaves. We discuss the following topics: indecomposability and faithful…

### Localizations of the category of $A_\infty$ categories and internal Homs

- Mathematics
- 2018

We prove that the localizations of the categories of dg categories, of cohomologically unital and strictly unital $A_\infty$ categories with respect to the corresponding classes of quasi-equivalences…

## References

SHOWING 1-10 OF 77 REFERENCES

### Uniqueness of dg enhancements for the derived category of a Grothendieck category

- MathematicsJournal of the European Mathematical Society
- 2018

We prove that the derived category of a Grothendieck abelian category has a unique dg enhancement. Under some additional assumptions, we show that the same result holds true for its subcategory of…

### Uniqueness of enhancement for triangulated categories

- Mathematics
- 2010

The paper contains general results on the uniqueness of a DG enhancement for trian- gulated categories. As a consequence we obtain such uniqueness for the unbounded categories of quasi-coherent…

### Perfect complexes on algebraic stacks

- MathematicsCompositio Mathematica
- 2017

We develop a theory of unbounded derived categories of quasi-coherent sheaves on algebraic stacks. In particular, we show that these categories are compactly generated by perfect complexes for stacks…

### Smashing subcategories and the telescope conjecture – an algebraic approach

- Mathematics
- 2000

Abstract.We prove a modified version of Ravenel’s telescope conjecture. It is shown that every smashing subcategory of the stable homotopy category is generated by a set of maps between finite…

### Deriving DG categories

- Mathematics
- 1994

— We investigate the (unbounded) derived category of a differential Z-graded category (=DG category). As a first application, we deduce a "triangulated analogue" (4.3) of a theorem of Freyd's [5],…

### Cohomological quotients and smashing localizations

- Mathematics
- 2003

The quotient of a triangulated category modulo a subcategory was defined by Verdier. Motivated by the failure of the telescope conjecture, we introduce a new type of quotients for any triangulated…

### An example of a non-Fourier–Mukai functor between derived categories of coherent sheaves

- MathematicsInventiones mathematicae
- 2019

Orlov’s famous representability theorem asserts that any fully faithful exact functor between the bounded derived categories of coherent sheaves on smooth projective varieties is a Fourier–Mukai…

### Generators and representability of functors in commutative and noncommutative geometry

- Mathematics
- 2002

We give a sufficient condition for an Ext-finite triangulated category to be saturated. Saturatedness means that every contravariant cohomological functor of finite type to vector spaces is…