Perfect complex

In algebra, a perfect complex of modules over a commutative ring "A" is an object in the derived category of "A"-modules that is quasi-isomorphic to a bounded complex of finite projective "A"-modules. A perfect module is a module that is perfect when it is viewed as a complex concentrated at degree zero. For example, if "A" is Noetherian, a module over "A" is perfect if and only if it has finite projective dimension.
Other characterizations.
Perfect complexes are precisely the compact objects in the unbounded derived category formula_1 of "A"-modules. They are also precisely the dualizable objects in this category.
A compact object in the ∞-category of (say right) module spectra over a ring spectrum is often called perfect; see also module spectrum.
Pseudo-coherent sheaf.
When the structure sheaf formula_2 is not coherent, working with coherent sheaves has awkwardness (namely the kernel of a finite presentation can fail to be coherent). Because of this, SGA 6 Expo I introduces the notion of a pseudo-coherent sheaf.
By definition, given a ringed space formula_3, an formula_2-module is called pseudo-coherent if for every integer formula_5, locally, there is a free presentation of finite type of length "n"; i.e., 
A complex "F" of formula_2-modules is called pseudo-coherent if, for every integer "n", there is locally a quasi-isomorphism formula_8 where "L" has degree bounded above and consists of finite free modules in degree formula_9. If the complex consists only of the zero-th degree term, then it is pseudo-coherent if and only if it is so as a module.
Roughly speaking, a pseudo-coherent complex may be thought of as a limit of perfect complexes.