User Zhaoting Wei

3 votes

0 answers

244 views

Reference Request: The Categorification of $\mathbb{Z}$ as cochain complexes of vector spaces

asked Sep 11, 2012 at 5:20

3 votes

0 answers

246 views

The multiplicative system in a symmetric monoidal category

asked Sep 27, 2012 at 5:53

3 votes

1 answer

508 views

The Hochschild cohomology of a variety "with coefficient" in a vector bundle

asked Sep 18, 2013 at 5:12

3 votes

1 answer

312 views

A question about the morphisms in the homotopy category of dg-Cat

asked May 13, 2015 at 14:10

3 votes

2 answers

623 views

How to show the following two definitions of homotopy monomorphism are equivalent?

asked May 13, 2015 at 16:15

3 votes

0 answers

422 views

What kind of ringed space $X$ has the property that a locally free sheaf is projective in Qcoh$(X)$?

asked Mar 17, 2015 at 20:42

3 votes

2 answers

1k views

An alternative definition of pseudo-coherent complex

asked Mar 20, 2015 at 15:33

3 votes

1 answer

376 views

Is $K^0(X)\to K_0(X)$ monomorphic for a noetherian scheme $X$?

asked Apr 17, 2015 at 1:42

3 votes

1 answer

575 views

What is the "higher version" of chain homotopy in singular homology?

asked Dec 13, 2013 at 22:53

3 votes

1 answer

211 views

Is the image of a idempotent morphism in $\mathcal{K}(\mathcal{A})$ defined in the naive way?

asked Mar 12, 2015 at 2:25

3 votes

0 answers

268 views

What's the relation of the Hecke algebra of a pair and the flag variety?

asked Feb 17, 2015 at 21:25

3 votes

0 answers

425 views

Do all full exceptional sequences of a triangulated category have the same length?

asked Oct 7, 2014 at 21:50

3 votes

1 answer

235 views

Is the cotangent complexes of groupoids bounded above by degree $1$?

asked Sep 7, 2014 at 20:59

3 votes

1 answer

381 views

Could we extend the Atiyah class to the sheaf of poly-vector fields to get a Poisson bracket?

asked Oct 2, 2013 at 5:47

3 votes

0 answers

102 views

Can we extend a homotopy invertible chain morphisms between complexes of sheaves from a closed subspace to the whole space?

asked Sep 15, 2015 at 3:36

3 votes

1 answer

516 views

For what kind of sheaves can we always extend a sheaf map from a closed subset to the whole space?

asked Sep 25, 2015 at 4:26

3 votes

0 answers

392 views

Is Carlos Simpson's Descent available online?

asked Dec 1, 2015 at 3:53

3 votes

3 answers

755 views

Is $Pic^0(X)$ of a curve of genus $\geq 1$ over a non-algebraically closed field still non-finitely generated?

asked Dec 19, 2015 at 16:54

3 votes

1 answer

164 views

Could $RHom(A,-)$ distinguish non-quasi-equivalent dg-categories?

asked Nov 15, 2016 at 3:12

3 votes

1 answer

214 views

How to find two non-isomorphic elliptic curves with isomorphic products with another elliptic curve?

asked Nov 17, 2016 at 4:38

3 votes

0 answers

538 views

Could we prove the flat base change theorem for cohomology via injective resolution?

asked May 24, 2017 at 16:26

3 votes

1 answer

467 views

Why do we need cofiltered condition on the index category in the definition of pro-categories?

asked May 1, 2017 at 16:07

3 votes

0 answers

84 views

Could we have the simplicial definition of equivariant derived category of sheaves with arrow direction inversed?

asked Jan 20, 2019 at 4:31

3 votes

1 answer

343 views

Is any element in $H^2_{et}(X,\mathcal{O}_X^*)$ locally trivial in the Zariski topology?

asked Oct 30, 2017 at 2:08

3 votes

0 answers

140 views

Do we have a transgression formula for the chern characters of quasi-isomorphic cochain complexes of vector bundles?

asked Mar 23, 2018 at 21:45

2 votes

0 answers

251 views

Is there a by-hand prove that $\Gamma(\mathbb{C}P^n,E)$ is finite dimensional for a holomorphic vector bundle $E$?

asked Feb 15, 2019 at 3:17

2 votes

1 answer

142 views

Is the algebra of Schwarz functions on a noncommutative torus the maximal algebra of smooth functions?

asked Apr 7, 2019 at 15:00

2 votes

1 answer

513 views

Does a natural transformation of functors induce a natural transformation between their right adjoints?

asked Nov 19, 2020 at 5:02

2 votes

0 answers

100 views

Could we construct an inverse transform for the equivalence $D^b(X)\to D^b(M)$ between a K3 surface and its moduli space of semistable sheaves?

asked May 10, 2017 at 22:47

2 votes

0 answers

248 views

What are the point-like objects in $D^b(X)$ when $X$ is an abelian variety?

asked Nov 2, 2016 at 2:12

Stack Exchange Network

168 Questions

Reference Request: The Categorification of $\mathbb{Z}$ as cochain complexes of vector spaces

The multiplicative system in a symmetric monoidal category

The Hochschild cohomology of a variety "with coefficient" in a vector bundle

A question about the morphisms in the homotopy category of dg-Cat

How to show the following two definitions of homotopy monomorphism are equivalent?

What kind of ringed space $X$ has the property that a locally free sheaf is projective in Qcoh$(X)$?

An alternative definition of pseudo-coherent complex

Is $K^0(X)\to K_0(X)$ monomorphic for a noetherian scheme $X$?

What is the "higher version" of chain homotopy in singular homology?

Is the image of a idempotent morphism in $\mathcal{K}(\mathcal{A})$ defined in the naive way?

What's the relation of the Hecke algebra of a pair and the flag variety?

Do all full exceptional sequences of a triangulated category have the same length?

Is the cotangent complexes of groupoids bounded above by degree $1$?

Could we extend the Atiyah class to the sheaf of poly-vector fields to get a Poisson bracket?

Can we extend a homotopy invertible chain morphisms between complexes of sheaves from a closed subspace to the whole space?

For what kind of sheaves can we always extend a sheaf map from a closed subset to the whole space?

Is Carlos Simpson's Descent available online?

Is $Pic^0(X)$ of a curve of genus $\geq 1$ over a non-algebraically closed field still non-finitely generated?

Could $RHom(A,-)$ distinguish non-quasi-equivalent dg-categories?

How to find two non-isomorphic elliptic curves with isomorphic products with another elliptic curve?

Could we prove the flat base change theorem for cohomology via injective resolution?

Why do we need cofiltered condition on the index category in the definition of pro-categories?

Could we have the simplicial definition of equivariant derived category of sheaves with arrow direction inversed?

Is any element in $H^2_{et}(X,\mathcal{O}_X^*)$ locally trivial in the Zariski topology?

Do we have a transgression formula for the chern characters of quasi-isomorphic cochain complexes of vector bundles?

Is there a by-hand prove that $\Gamma(\mathbb{C}P^n,E)$ is finite dimensional for a holomorphic vector bundle $E$?

Is the algebra of Schwarz functions on a noncommutative torus the maximal algebra of smooth functions?

Does a natural transformation of functors induce a natural transformation between their right adjoints?

Could we construct an inverse transform for the equivalence $D^b(X)\to D^b(M)$ between a K3 surface and its moduli space of semistable sheaves?

What are the point-like objects in $D^b(X)$ when $X$ is an abelian variety?