45 Intuition about the cotangent complex? 2009-10-26T13:00:24.520

44 What does a projective resolution mean geometrically? 2009-10-23T16:52:26.897

33 What (if anything) unifies stable homotopy theory and Grothendieck's six functors formalism? 2014-06-08T00:08:25.230

32 A down-to-earth introduction to the uses of derived categories 2010-09-21T14:51:01.377

31 Simplicial objects 2009-10-16T01:17:48.863

31 How to think about model categories? 2009-10-23T21:00:31.737

31 What is a deformation of a category? 2009-11-13T14:59:36.503

30 How do I know the derived category is NOT abelian? 2010-02-18T02:27:19.303

27 What is a triangle? 2016-12-18T05:14:38.977

25 Is there a Grothendieck-Riemann-Roch type of theorem generalizing Grothendieck's Lefschetz trace formula 2010-11-21T13:46:52.107

25 Complete the following sequence: point, triangle, octahedron, . . . in a dg-category 2016-04-17T21:33:26.763

24 Which properties of a variety are detected by its derived category of coherent sheaves? 2015-01-12T10:35:33.503

22 determinant of a perfect complex 2009-11-29T09:55:14.073

22 Heuristic behind the Fourier-Mukai transform 2009-12-26T23:59:36.100

22 Why are derived categories natural places to do deformation theory? 2012-11-01T00:47:44.990

20 Homotopy-theoretic derived Morita equivalences 2013-07-03T17:31:23.630

20 Why would one "attempt" to define points of a motive as $\operatorname{Ext}^1(\mathbb{Q}(0),M)$? 2015-09-28T00:34:04.267

20 Example of an additive functor admitting no right derived functor 2017-03-20T11:18:06.930

19 Examples for Decomposition Theorem 2009-10-22T21:59:48.107

19 Is the Fukaya category "defined"? 2009-10-27T22:00:44.263

18 distinguished triangles and cohomology 2009-10-31T09:47:40.333

18 Generating the derived category with line bundles 2010-08-17T12:32:07.497

17 Derived categories and homotopy categories 2009-10-12T19:15:48.873

17 Is there an Infinite dimensional sheaf theory for analysis on manifolds? 2017-08-05T17:04:30.363

14 Why does the naive definition of compactly supported étale cohomology give the wrong answer? 2010-04-11T23:59:40.220

14 Intuition about the triangulation of a homotopy category K(A) 2010-10-21T23:03:54.320

14 The derived category of the heart of a t-structure 2012-11-14T20:33:48.047

14 How can one interpret homology and Stokes' Theorem via derived categories? 2013-06-23T19:17:40.797

14 Constructive homological algebra in HoTT 2017-11-22T23:18:18.347

13 Derived functors vs universal delta functors 2009-10-28T02:29:06.287

13 When is every "solid" perfect complex faithful? 2010-04-19T20:31:57.177

13 Sheaves without global sections 2010-10-25T22:24:23.210

13 What is the relation between the Lie bracket on $TX$ as commutator and that coming from the Atiyah class? 2013-09-26T15:50:47.503

13 Multiplicativity twisted Hochschild Kostant Rosenberg isomorphism 2016-09-05T21:27:28.720

13 Why do people study unbounded derived category of quasi-coherent sheaves rather than focus on bounded derived category of coherent sheaves? 2017-03-12T19:41:16.620

12 Categories which are not compactly generated 2009-11-11T01:11:40.930

12 References for a certain generalization of Hochschild cohomology? 2009-12-08T21:24:13.840

12 What is a flop (and when are they conjectured to give derived equivalences)? 2010-06-14T14:25:05.120

12 Analytic Torsion in the Derived Category 2011-03-14T20:30:33.813

12 Derived categories of (coherent) sheaves of modules: exceptional images, gluing, and proper descent? 2011-05-27T10:07:09.277

12 Fiber functors to derived categories 2012-01-20T06:57:16.823

12 The derived category of integral representations of a Dynkin quiver. 2012-04-25T15:12:25.760

12 Fullness of pullback functor in algebraic geometry 2012-07-12T18:38:50.287

12 Can Enriques Surfaces have non-trivial TWISTED Fourier-Mukai partners? 2015-02-19T11:05:08.903

11 Freyd-Mitchell for triangulated categories? 2009-10-20T15:34:36.770

11 When do six operations work? 2009-11-01T09:03:29.193

11 What is the Hochschild cohomology of the dg category of perfect complexes on a variety? 2011-02-12T16:41:49.580

11 Fourier-Mukai functors being identity on objects 2014-12-03T17:55:49.967

11 An example of an object in $D^b_{\text{coh}}(\mathbb{P}^2)$ which is not formal 2015-02-07T16:22:57.530

11 Homotopy property of constructible sheaves on stratified spaces 2016-04-11T12:01:22.893

11 Categorical mapping class group action 2017-03-03T03:40:00.760

11 Can "ampleness" be detected inside the derived category? 2017-11-12T22:49:36.027

10 On the derived category of constructible étale sheaves 2012-12-05T02:44:54.700

10 McKay correspondence and tensor products 2013-03-11T03:22:47.303

10 what is the universal cover of GL(2,R)? 2016-04-28T22:18:50.620

10 K-stability is invariant under D-equivalency 2017-10-21T14:08:32.253

9 Compact generation for modular representations 2009-11-11T02:37:51.987

9 Verdier duality via Brown representability? 2010-02-17T07:37:59.810

9 How to write down the determinant of a quasi-isomorphism? 2010-04-22T23:06:57.020

9 Are the underlying undirected graphs of two mutation-equivalent acylic quivers isomorphic? 2010-06-04T12:32:11.953

9 Derived Physics 2010-06-11T15:17:27.803

9 Do I need to know what an infinity-Gerstenhaber algebra is, and if so, what is it? 2011-04-29T06:07:03.650

9 got any tricks to build up t-structures on derived categories? 2012-08-02T08:31:39.643

9 Recovering an abelian category out of its derived category 2013-02-13T20:17:53.703

9 Why is proving fully-faithfulness of an integral functor locally analytically sufficient? 2013-08-06T13:59:08.590

9 Are $D^b_{coh}(X)$ and $D^b(Coh(X))$ derived equivalent? 2014-02-28T15:31:42.350

9 derived categories as presentable DG-categories 2016-01-11T15:23:21.140

9 Is the perfectness of Fourier-Mukai kernels proved by Toen? 2017-01-01T01:16:43.960

9 Stable homotopy category of complexes of sheaves 2017-01-27T10:13:58.893

9 Vanishing natural transformation exact triangle 2018-02-13T18:20:07.500

8 group of Yoneda extensions and the EXT groups defined via derived category 2010-09-24T23:23:56.353

8 l-adic vs complex Perverse Sheaves 2011-10-18T12:27:18.320

8 The composition of derived functors - commutation fails hazardly? 2011-12-20T14:54:54.187

8 Evens norm as a derived functor 2012-12-23T06:10:02.790

8 Derived categories of toric varieties and convex geometry 2013-06-06T19:33:37.267

8 Equivariant motivic sheaves 2014-06-10T14:06:56.027

8 What is the applications of the dg-enhancements of derived categories of sheaves 2015-04-04T01:22:50.643

8 Is there a (satisfying) proof that cellular cohomology is isomorphic to simplicial cohomology that doesn't use relative cohomlogy? 2015-05-13T22:05:01.930

8 When the restriction of a derived functor to a subcategory is the derived functor of the restriction 2015-07-15T18:36:23.617

8 List of known Fourier Mukai partners? 2015-12-10T11:13:27.717

8 Non-Standard Derived Equivalences of Non-Flat Algebras 2016-02-03T17:17:15.730

8 A Naive Question on Mixed Motives and Mixed Hodge Structures 2017-05-30T20:34:08.820

7 Is an irreducible holomorphic symplectic manifold a simple Lie algebra? 2010-03-05T14:54:59.977

7 Classification of t-structures in derived category of R-mod? 2010-07-15T15:48:49.143

7 Lifting isomorphisms between derived categories 2012-06-17T08:42:35.863

7 Derived category of varieties and derived category of quiver algebras 2012-11-25T22:03:16.877

7 A question on the "natural metric" on the space of Bridgeland stability condition 2013-01-02T23:07:14.920

7 Not isomorphic varieties with isomorphic tilting algebras 2013-01-10T12:44:12.460

7 What is a good reference (preferably thorough) for the Derived Category of a scheme/orbifold/stack? 2013-05-10T15:04:04.027

7 Derived category of toroidal varieties 2013-06-06T03:33:25.427

7 Derived categories of singular varieties 2013-12-04T21:16:23.977

7 Idea and intuition behind Penrose transform 2014-09-07T10:23:20.937

7 flatness and derived completion 2015-02-28T21:47:55.927

7 Injective model structure on sheaves of bounded complexes of $A$-modules 2015-08-30T18:33:38.860

7 What is integration along the fibers in D-module theory? 2016-10-06T18:33:57.197

7 Smoothness of a projective variety via the derived category 2017-01-19T11:02:34.867

7 Categorification of definitions in the context of the derived category of quasi-coherent sheaves 2017-01-24T19:50:10.203

7 Automorphism that the Fukaya category is "blind" to 2017-03-03T02:41:54.550

7 Identifying and reconstructing the derived category from its auto-equivalences 2017-03-21T05:01:40.303