5
votes
Accepted
A pushout diagram of derived categories coming from an open cover of schemes
I don't know if this answers your question, but you seem to have outlined yourself the whole phenomenon yourself.
The point is that while $Cat_{st}$ (or $Cat_{dg}$) is not itself stable, it has a ...
5
votes
Concrete examples of derived categories
One way to concretely describe derived categories is via the framework of model categories, and from the comments, it sounds like the OP is satisfied with this approach. Let $R$ be a commutative ring ...
4
votes
Accepted
Pushforward of exceptional vector bundle is spherical for local P^2
As $i$ is a divisorial embedding, there is a distinguished triangle
$$
i^*i_*\mathcal{E} \to \mathcal{E} \to \mathcal{E} \otimes \mathcal{O}(3)[2]
$$
(here $\mathcal{O}(3)$ in the last term is just ...
2
votes
Accepted
Pullback morphism of a hyperplane inclusion is zero in the derived category
You are asking whether a specific element of ${\rm Hom}_{D^b({\rm Ab})}(\mathbb Z[-2n], \mathbb Z[-2n-2])$ is zero. But this group is ${\rm Ext}^2_{\rm Ab}(\mathbb Z, \mathbb Z) = 0$. (Because $\...
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