All Questions
7
questions
5
votes
1
answer
361
views
Which complexes of coherent sheaves can be presented as countable homotopy limits of perfect complexes?
Let $X$ be a noetherian scheme (actually, I need the case where $X$ is proper over an affine scheme), $C$ is an object of the derived category $D_{coh}(X)$ of coherent sheaves on $X$. Under which ...
- 16.7k
2
votes
1
answer
246
views
Semi-orthogonal decompositions over singular schemes
Where can I find any more or less explicit semi-orthogonal decompositions of derived categories of perfect complexes or of bounded derived categories for singular schemes that are proper over a ring R?...
- 16.7k
3
votes
0
answers
148
views
Bounded derived categories of which smooth projectives possess bounded t-structures whose hearts are categories of modules?
I am interested in $P$ that is smooth and proper over a field and such that the derived category of coherent sheaves $D^b(P)$ possesses a $t$-structure whose heart is the category of finitely ...
- 16.7k
4
votes
0
answers
303
views
Which derived categories of coherent sheaves are equivalent (or "$t$-related") to derived categories of rings?
As far as I understand, it was Beilinson who proved that the bounded derived category of coherent sheaves $D^b(\mathbb{P}^n)$ is equivalent to the bounded derived category of a certain (non-...
- 16.7k
3
votes
1
answer
279
views
Is there a notion of injective, projective, flat, dimension for a differential graded algebra?
Given a differential graded algebra $(A_\bullet,d)$, is there a well-defined notion of a K-injective, K-projective, K-flat dimension of a differential graded module, or even of the category of ...
- 1,706
5
votes
1
answer
399
views
Could we extend the exact sequence $K^0(X)\to K_0(X)\to K_0(D_{sg}(X))\to 0$ to the left?
Let $X$ be a variety over a field $k$. We have the bounded derived category of coherent sheaves $D^b_{coh}(X)$ and the derived category of perfect complex $Perf(X)$. It is clear that $Perf(X)$ is a ...
- 8,767
2
votes
1
answer
339
views
Is $K^0(X)\to K_0(X)$ monomorphic for a noetherian scheme $X$?
This question is related to the MO questions What is the difference between Grothendieck groups K_0(X) vs K^0(X) on schemes? and Does a fully faithful functor between triangulated categories induce ...
- 8,767