Homotopy equivalences and Grothendieck duality over rings with finite Gorenstein weak global dimension

Let R be a ring with Gwgldim$\left(R\right)<\infty$. We obtain a triangle-equivalence $\text{K}\left(R\text{-}\text{GProj}\right)\simeq \text{K}\left(R\text{-}\text{GInj}\right)$ which restricts to a triangle-equivalence $\text{K}\left(R\text{-}\text{Proj}\right)$ $\simeq \text{K}\left(R\text{-}\text{Inj}\right)$. This class of rings includes, among others, (left) Gorenstein rings, Ding–Chen rings and the more general Gorenstein n-coherent rings ($n\in N\cup \{\infty \},n\ge 2$). As application, we establish some triangle-equivalences of Grothendieck duality over Ding–Chen rings and Gorenstein n-coherent rings.