perfect dg-modules

The *perfect dg-modules* over a dg-category are the compact objects of its derived dg-category.

A dg-module $M \in D(T)$ is **perfect** if it is in the full sub-dg-category generated by the pretriangulated envelope $tri(A)$ under direct summands.

We will write $perf(T) \subset D(T)$ for the full sub-dg-category of $D(T)$ spanned by perfect dg-modules. This is a pretriangulated sub-dg-category.

By the explicit description of the pretriangulated envelope, one gets

A dg-module $M \in D(T)$ is perfect if and only if it is it is in the full sub-dg-category of $D(T)$ generated by the finitely generated semi-free dg-modules under direct summands.

Section 2.3 of

- Dmitri Orlov,
*Smooth and proper noncommutative schemes and gluing of DG categories*, arXiv:1402.7364.

Paragraph 3.5 of

- Bernhard Keller,
*On differential graded categories*, arXiv:math/0601185.

Created on January 7, 2015 at 12:11:16. See the history of this page for a list of all contributions to it.