Definition
Let \(F\) be an Artin stack and let \(E^\bullet \in \mathcal D_F^{\leq 0}\). We say that \(E^\bullet\) is of perfect amplitude if there exists \(n\geq 0\) such that \(E^\bullet\) is locally isomorphic to \[E^{-n} \to ... \to E^0\] where for all \(i \in \{-n,...,0\}\), \(E^i\) is locally free sheaf.