User Zhaoting Wei

2 votes

0 answers

276 views

Is the dg-nerve functor a Quillen equivalence?

asked Aug 3, 2015 at 19:38

2 votes

1 answer

569 views

Why $k[x,y]$ is not a formally smooth algebra?

asked Jun 15, 2016 at 3:27

2 votes

1 answer

457 views

Could we construct the Jacobian variety of a smooth curve $C$ with genus $>2$ from its derived category $D(C)$?

asked Oct 22, 2013 at 4:08

2 votes

0 answers

166 views

How to understand $\mathcal{L}BG \simeq G/^{\text{ad}}G$ in term of simplicial sets?

asked May 30, 2014 at 0:41

2 votes

0 answers

138 views

Is there any numerical obstruction for all perfect complexes on a scheme being strictly perfect?

asked Nov 4, 2014 at 17:54

2 votes

0 answers

866 views

How to prove that any perfect complex on an affine scheme is strictly perfect?

asked Mar 9, 2015 at 22:12

2 votes

1 answer

619 views

Does a fully faithful functor between triangulated categories induce embedding of their Grothendieck groups?

asked Apr 16, 2015 at 16:58

2 votes

0 answers

130 views

Does it require Reedy fibrancy when we want the totalization to be weakly equivalent to the homotopy limit?

asked Jul 3, 2015 at 14:14

2 votes

2 answers

799 views

Could we extend any line bundle on the smooth part of a singular curve to a line bundle on the whole curve?

asked Apr 30, 2015 at 20:07

2 votes

0 answers

416 views

Do we have the following "devissage commutative diagram" in K-theory?

asked May 1, 2015 at 14:23

2 votes

1 answer

224 views

The orbit $(G\cdot X) \cap \mathfrak{t}$ for $X\in \mathfrak{t}$ singular

asked Jun 20, 2013 at 3:27

2 votes

1 answer

536 views

Kasparov's Dirac element and the index map

asked Oct 24, 2012 at 17:32

2 votes

2 answers

721 views

Does $G/H$ (quotient of a real semisimple Lie group by a Cartan subgroup) have a natural symplectic structure?

asked Aug 31, 2012 at 4:38

2 votes

1 answer

256 views

The real group orbits on the flag variety always contains the holomorphic directions?

asked Sep 1, 2012 at 7:05

2 votes

1 answer

450 views

Can we compute the Hochschild cohomology for $k[x]$ through the Hochschild complex?

asked Feb 17, 2022 at 4:26

2 votes

0 answers

244 views

Do we have a left adjoint of $i^*$ for a closed immersion $i$?

asked Jun 21, 2022 at 16:22

2 votes

1 answer

239 views

How to complete $i^i_\mathcal{F}\to \mathcal{F}$ into an exact triangle for a smooth divisor $i: X\hookrightarrow Y$?

asked Jun 30, 2022 at 4:11

2 votes

0 answers

129 views

Is the deformation of a $C^{\infty}$-manifold over Artin local algebra trivial?

asked Oct 24 at 14:46

2 votes

0 answers

278 views

Is an infinite direct sum of quasi-coherent $\mathcal{O}_X$-modules quasi-coherent on a complex manifold?

asked Aug 18, 2023 at 22:52

1 vote

0 answers

100 views

Is an isomorphism between holomorphic vector bundles still holomorphic with respect to a deformation parameter?

asked Jul 4, 2023 at 4:26

1 vote

0 answers

86 views

Do we have a Grauert-Fischer theorem for non-trivial families?

asked Jul 7, 2023 at 13:57

1 vote

0 answers

312 views

Can we classify two dimensional complex vector bundles over $\mathbb{R}P^2$?

asked May 28, 2022 at 4:02

1 vote

0 answers

97 views

Do we have an equivariant Newlander-Nirenberg theorem for finite group action?

asked Jan 23, 2023 at 15:54

1 vote

0 answers

133 views

Does the Mukai's lemma hold for non-algebraic $K3$ surfaces?

asked Oct 16, 2021 at 5:38

1 vote

0 answers

276 views

Does the Hochschild cohomology of an $A_{\infty}$-algebra have an algebra structure?

asked Jan 26, 2022 at 2:27

1 vote

1 answer

219 views

What is the cohomology of the $C^{\infty}$-Koszul complex on $\mathbb{C}^2$?

asked Dec 8, 2021 at 5:39

1 vote

1 answer

164 views

Find an action of $\mathbb{Z}/2$ on $\mathbb{C}P^1$ which is compatible with the fraction linear transform of $SL(2,\mathbb{R})$

asked Jul 26, 2012 at 18:21

1 vote

1 answer

325 views

Do we have the following isomorphism for $\mathcal{Ext}$?

asked Sep 10, 2013 at 19:02

1 vote

0 answers

146 views

Is there any explicit result on the triangulated category of singularities of a curve?

asked Apr 28, 2015 at 12:59

1 vote

0 answers

203 views

Is there any computation of $K^0(X)$ and $K_0(X)$ for a singular curve $X$?

asked Apr 23, 2015 at 22:19

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168 Questions

Is the dg-nerve functor a Quillen equivalence?

Why $k[x,y]$ is not a formally smooth algebra?

Could we construct the Jacobian variety of a smooth curve $C$ with genus $>2$ from its derived category $D(C)$?

How to understand $\mathcal{L}BG \simeq G/^{\text{ad}}G$ in term of simplicial sets?

Is there any numerical obstruction for all perfect complexes on a scheme being strictly perfect?

How to prove that any perfect complex on an affine scheme is strictly perfect?

Does a fully faithful functor between triangulated categories induce embedding of their Grothendieck groups?

Does it require Reedy fibrancy when we want the totalization to be weakly equivalent to the homotopy limit?

Could we extend any line bundle on the smooth part of a singular curve to a line bundle on the whole curve?

Do we have the following "devissage commutative diagram" in K-theory?

The orbit $(G\cdot X) \cap \mathfrak{t}$ for $X\in \mathfrak{t}$ singular

Kasparov's Dirac element and the index map

Does $G/H$ (quotient of a real semisimple Lie group by a Cartan subgroup) have a natural symplectic structure?

The real group orbits on the flag variety always contains the holomorphic directions?

Can we compute the Hochschild cohomology for $k[x]$ through the Hochschild complex?

Do we have a left adjoint of $i^*$ for a closed immersion $i$?

How to complete $i^i_\mathcal{F}\to \mathcal{F}$ into an exact triangle for a smooth divisor $i: X\hookrightarrow Y$?

Is the deformation of a $C^{\infty}$-manifold over Artin local algebra trivial?

Is an infinite direct sum of quasi-coherent $\mathcal{O}_X$-modules quasi-coherent on a complex manifold?

Is an isomorphism between holomorphic vector bundles still holomorphic with respect to a deformation parameter?

Do we have a Grauert-Fischer theorem for non-trivial families?

Can we classify two dimensional complex vector bundles over $\mathbb{R}P^2$?

Do we have an equivariant Newlander-Nirenberg theorem for finite group action?

Does the Mukai's lemma hold for non-algebraic $K3$ surfaces?

Does the Hochschild cohomology of an $A_{\infty}$-algebra have an algebra structure?

What is the cohomology of the $C^{\infty}$-Koszul complex on $\mathbb{C}^2$?

Find an action of $\mathbb{Z}/2$ on $\mathbb{C}P^1$ which is compatible with the fraction linear transform of $SL(2,\mathbb{R})$

Do we have the following isomorphism for $\mathcal{Ext}$?

Is there any explicit result on the triangulated category of singularities of a curve?

Is there any computation of $K^0(X)$ and $K_0(X)$ for a singular curve $X$?