User Zhaoting Wei

21 votes

0 answers

1k views

Can we describe equivariant vector bundles of free group action in terms of descent theory (Barr-Beck theorem)?

asked Aug 27, 2012 at 3:44

20 votes

2 answers

3k views

Is there any "deep" relation between the localization theorem of equivariant cohomology and the localization theorem of equivariant K-theory

asked Sep 10, 2012 at 16:22

20 votes

2 answers

4k views

What is the significance that the Springer resolution is a moment map?

asked Jul 16, 2012 at 22:16

16 votes

5 answers

2k views

About the intrinsic definition of the Weyl group of complex semisimple Lie algebras

asked Aug 2, 2012 at 2:10

15 votes

4 answers

2k views

What is the relation between the Lie bracket on $TX$ as commutator and that coming from the Atiyah class?

asked Sep 26, 2013 at 15:50

15 votes

1 answer

3k views

Is a locally free sheaf projective in the category of $\mathcal{O}_X$-modules when $X$ is an affine scheme?

asked Mar 17, 2015 at 16:54

14 votes

1 answer

2k views

What is the applications of the dg-enhancements of derived categories of sheaves

asked Apr 4, 2015 at 1:22

14 votes

3 answers

768 views

Is $C^{\infty}(\mathbb{R}^{m+n})$ a flat module over $C^{\infty}(\mathbb{R}^{m})$?

asked Dec 15, 2019 at 3:17

13 votes

0 answers

740 views

Why do people study unbounded derived category of quasi-coherent sheaves rather than focus on bounded derived category of coherent sheaves?

asked Mar 12, 2017 at 19:41

12 votes

1 answer

2k views

Is the derived category of $A$-dg-modules as a dg-category coincide with the ordinary definition of derived category?

asked Jan 24, 2018 at 2:16

12 votes

2 answers

2k views

What is descent data (of higher categories), conceptually?

asked Jul 6, 2015 at 15:36

12 votes

1 answer

648 views

An example of an object in $D^b_{\text{coh}}(\mathbb{P}^2)$ which is not formal

asked Feb 7, 2015 at 16:22

11 votes

1 answer

387 views

Is there any relation between the simplicial $S^1$ and the Hochschild homology of a noncommutative algebras

asked Mar 6, 2014 at 0:43

10 votes

0 answers

740 views

What is Quillen's contribution to index theorem?

asked May 7, 2013 at 3:51

10 votes

0 answers

212 views

Does the category of $G$-equivariant sheaves have enough injectives?

asked Jan 11, 2019 at 15:14

10 votes

3 answers

646 views

Is the tensor product of two infinite dimensional objects in the BGG category $\mathcal{O}$ of a semisimple Lie algebra always not in $\mathcal{O}$?

asked Sep 15, 2019 at 11:17

10 votes

1 answer

670 views

Do we have "cancellation law" for products of varieties

asked Nov 8, 2016 at 15:35

10 votes

1 answer

714 views

Why do the model structures on dg-algebras and on dg-categories are not compatible?

asked Jul 31, 2015 at 15:42

9 votes

0 answers

332 views

Is the perfectness of Fourier-Mukai kernels proved by Toen?

asked Jan 1, 2017 at 1:16

9 votes

2 answers

535 views

A question about the Tannaka-Krein reconstruction of finite groups

asked Oct 11, 2019 at 13:50

9 votes

0 answers

198 views

Does a morphism which induces an isomorphism between Hochschild homology also induce an isomorphism between cyclic homology?

asked Apr 27, 2019 at 9:43

9 votes

1 answer

349 views

Does $X\times Y$ have the resolution property if both $X$ and $Y$ have?

asked Oct 16, 2021 at 5:55

8 votes

1 answer

320 views

Do chain homotopic maps between dg-algebras induce "same" maps on dg-modules

asked Mar 19, 2017 at 21:31

8 votes

2 answers

658 views

Is dgCat a category or a 2-category?

asked Sep 29, 2015 at 4:45

8 votes

1 answer

375 views

Do we have a "topological assembly map" in the Baum-Connes conjecture?

asked Jun 8, 2013 at 4:17

8 votes

3 answers

704 views

What is the categorical significance of the trivial $\mathfrak{g}$-module in the category of $\mathfrak{g}$-mod?

asked Sep 21, 2013 at 6:06

8 votes

3 answers

1k views

Is there a categorification of topological K-theory?

asked Aug 4, 2012 at 20:09

8 votes

1 answer

1k views

Can we define the tensor product in the derived category $D^b_{\text{coh}}(X)$ just from $D^b_{\text{coh}}(X)$ in certain cases?

asked Oct 1, 2013 at 0:36

8 votes

1 answer

2k views

Is the derived category of perfect complexes idempotent complete?

asked Mar 27, 2015 at 2:56

7 votes

1 answer

1k views

What's the relation between the heat kernel proof of the index theorem and deformation quantization?

asked Oct 6, 2013 at 2:07

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168 Questions

Can we describe equivariant vector bundles of free group action in terms of descent theory (Barr-Beck theorem)?

Is there any "deep" relation between the localization theorem of equivariant cohomology and the localization theorem of equivariant K-theory

What is the significance that the Springer resolution is a moment map?

About the intrinsic definition of the Weyl group of complex semisimple Lie algebras

What is the relation between the Lie bracket on $TX$ as commutator and that coming from the Atiyah class?

Is a locally free sheaf projective in the category of $\mathcal{O}_X$-modules when $X$ is an affine scheme?

What is the applications of the dg-enhancements of derived categories of sheaves

Is $C^{\infty}(\mathbb{R}^{m+n})$ a flat module over $C^{\infty}(\mathbb{R}^{m})$?

Why do people study unbounded derived category of quasi-coherent sheaves rather than focus on bounded derived category of coherent sheaves?

Is the derived category of $A$-dg-modules as a dg-category coincide with the ordinary definition of derived category?

What is descent data (of higher categories), conceptually?

An example of an object in $D^b_{\text{coh}}(\mathbb{P}^2)$ which is not formal

Is there any relation between the simplicial $S^1$ and the Hochschild homology of a noncommutative algebras

What is Quillen's contribution to index theorem?

Does the category of $G$-equivariant sheaves have enough injectives?

Is the tensor product of two infinite dimensional objects in the BGG category $\mathcal{O}$ of a semisimple Lie algebra always not in $\mathcal{O}$?

Do we have "cancellation law" for products of varieties

Why do the model structures on dg-algebras and on dg-categories are not compatible?

Is the perfectness of Fourier-Mukai kernels proved by Toen?

A question about the Tannaka-Krein reconstruction of finite groups

Does a morphism which induces an isomorphism between Hochschild homology also induce an isomorphism between cyclic homology?

Does $X\times Y$ have the resolution property if both $X$ and $Y$ have?

Do chain homotopic maps between dg-algebras induce "same" maps on dg-modules

Is dgCat a category or a 2-category?

Do we have a "topological assembly map" in the Baum-Connes conjecture?

What is the categorical significance of the trivial $\mathfrak{g}$-module in the category of $\mathfrak{g}$-mod?

Is there a categorification of topological K-theory?

Can we define the tensor product in the derived category $D^b_{\text{coh}}(X)$ just from $D^b_{\text{coh}}(X)$ in certain cases?

Is the derived category of perfect complexes idempotent complete?

What's the relation between the heat kernel proof of the index theorem and deformation quantization?