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Results tagged with derived-categories
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user 2503
For questions about the derived categories of various abelian categories and questions regarding the derived category construction itself.
3
votes
Accepted
When is a sheaf coherent if its image under a Fourier-Mukai transform is coherent?
Your proof works in the derived case as well.
That is, assume smoothness so that $D^bCoh$ is identified with the full subcategory of compact objects (in general the argument will apply to the subcate …
- 5,901
8
votes
Accepted
Could we extend the exact sequence $K^0(X)\to K_0(X)\to K_0(D_{sg}(X))\to 0$ to the left?
The exact sequence of triangulated categories
$$ Perf(X)\to D^b_{coh}(X)\to D_{sg}(X) $$
may be lifted to an exact sequence of stable $\infty$-categories or dg-categories in the sense of BGT: choose …
- 5,901
15
votes
Accepted
What is the applications of the dg-enhancements of derived categories of sheaves
It is hard to know where to begin! A general principle is that as long as you are only concerned with the derived category of a single variety, it is generally sufficient to consider it as a triangul …
- 5,901