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A differential graded category is a category enriched over complexes of modules for some commutative ring.

4 votes
1 answer
330 views

Reference request: category of sheaves of O-modules with coherent cohomology

Suppose $X$ is a smooth algebraic variety (say, in characteristic $0$). It's a folklore result that $D^b\text{Coh}(X)$ is equivalent to the derived category of complexes of sheaves of $\mathcal{O}_X$- …
Dmitry Vaintrob's user avatar
3 votes
Accepted

Perfect DG modules

Well by definition a DG module $X$ is perfect iff it is a direct summand of a module which is a finite iterated extension of free modules (it's then a nontrivial result that this property is the same …
Dmitry Vaintrob's user avatar