On dimension theory for complexes

Passage from the category of modules to the derived category gives insight into some classical results of homological dimension theory, and also yields a proof of the nondegeneracy of the Yoneda multiplication $\operatorname{Ext}_A^p(k,\,\cdot\,)\times\operatorname{Ext}_A^{n-p}(\,\cdot\,,k)\to\operatorname{Ext}_A^n(k,k)=k$, where the argument is a noetherian module (or a finite complex with noetherian homology) and $A$ is a regular local ring.
Bibliography: 9 titles.