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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.
A compact object in the ∞-category of (say right) module spectra over a ring spectrum is often called perfect; 〔http://www.math.harvard.edu/~lurie/281notes/Lecture19-Rings.pdf〕 see also module spectrum.
== See also ==
*Hilbert–Burch theorem
*Dualizable object
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