A perfect complex over a commutative ring is a perfect module over the Eilenberg-Mac Lane spectrum . Under the stable Dold-Kan correspondence, perfect complexes correspond to bounded chain complexes of finitely generated projective modules.
Viewing commutative rings as affine schemes, this definition generalizes to arbitrary stacks. In this generality, perfect modules still coincide with the dualizable objects, but not always with the compact objects. The latter does hold for quasi-compact quasi-separated schemes by work of Thomason, Neeman, Bondal-Van den Bergh.
For instance (Stacks Project, 07LT).
|geometry||monoidal category theory||category theory|
|perfect module||(fully-)dualizable object||compact object|
R. Thomason, T. Trobaugh, Higher algebraic K-theory of schemes and of derived categories, in The Grothendieck Festschrift, Vol. III (1990), pp. 247-436.
Amnon Neeman, The Grothendieck duality theorem via Bousfield’s techniques and Brown representability, J. Amer. Math. Soc., vol. 9, no. 1, 1996, pp. 205-236.