Koszul duality for compactly generated derived categories of second kind

Abstract

For any dg algebra $A$ we construct a closed model category structure on dg $A$-modules such that the corresponding homotopy category is compactly generated by dg $A$-modules that are finitely generated and free over $A$ (disregarding the differential). We prove that this closed model category is Quillen equivalent to the category of comodules over a certain, possibly nonconilpotent dg coalgebra, a so-called extended bar construction of $A$. This generalises and complements certain aspects of dg Koszul duality for associative algebras.

Updated to the published version; in addition the proof of Theorem 3.10 has been corrected

References in corpus (4)

• Coherent rings, fp-injective modules, dualizing complexes, and covariant Serre-Grothendieck duality
• Maurer-Cartan moduli and theorems of Riemann-Hilbert type
• On the (non)vanishing of some "derived" categories of curved dg algebras
• Gauge equivalence for complete $L_{\infty }$-algebras

Cited by in corpus (1)

• Differential graded Koszul duality: an introductory survey