Lemma 109.68.1. There exists a differential graded algebra $(A, \text{d})$ and a compact object $E$ of $D(A, \text{d})$ such that $E$ cannot be represented by a finite and graded projective differential graded $A$-module.

Proof. See discussion above. $\square$

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).