Some adjoints in homotopy categories
Let \(R\) be a ring. Let \({\mathcal K}(R\text{-Flat})\) (\({\mathcal K}(R\text{-Proj})\)) denote the homotopy category of cochain complexes of flat, (respectively, projective) \(R\)-modules. In a previous paper [see Invent. Math. 174, No.~2, 255--308 (2008; Zbl 1184.18008)], the author proved that \({\mathcal K}(R\text{-Proj})\) is a Verdier quotient of \({\mathcal K}(R\text{-Flat})\). Let \(j^*:{\mathcal K}(R\text{-Flat})\to {\mathcal K}(R\text{-Proj})\) denote the quotient functor. The main theorem in the paper proves that \(j^*\) has a right adjoint \(j_*\). The author mentions that this theorem has a generalization to (non-affine) schemes.
scientific article; zbMATH DE number 5712771
scientific article