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Results tagged with derived-categories
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user 78824
For questions about the derived categories of various abelian categories and questions regarding the derived category construction itself.
9
votes
2
answers
806
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What is integration along the fibers in D-module theory?
In Hotta, Takeuchi, Tanisaki's book on "D-modules, Perverse Sheaves, and Representation theory", for a morphism of smooth algebraic varieties $f:X \to Y$, they use the notation
$$
\int_f:D^b(D_X^{op}) …
- 1,716
3
votes
1
answer
281
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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 differe …
- 1,716
2
votes
0
answers
226
views
What is the motivation behind the definition for a smooth differential graded category?
Let $\mathcal{A}$ be an $\mathbb{F}$-linear differential graded category. It is said to be smooth if it is a perfect complex over the differential graded category $\mathcal{A}^\circ\otimes_\mathbb{F}\ …
- 1,716
1
vote
Examples for Decomposition Theorem
A nice example of the decomposition theorem for a proper morphism of smooth varieties is the blowup of the points $p_i$ lying at the intersection of two plane curves; that is, let $f, g \in \mathbb{C} …
- 1,716