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.[1] 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; [2] see also module spectrum.
See also
- Hilbert–Burch theorem
- Dualizable object
References
External links
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