Journal of the
Korean Mathematical Society JKMS

We describe the Gorenstein derived categories of Gorenstein rings via the homotopy categories of Gorenstein injective modules. We also introduce the concept of Gorenstein cosilting complexes and study its basic properties. This concept is generalized by cosilting complexes in relative homological methods. Furthermore, we investigate the existence of the relative version of the Bongartz's theorem and construct a Bongartz's complement for a Gorenstein precosilting complex.

Keywords: Gorenstein injective module, Gorenstein cosilting complex, Gorenstein derived category

MSC numbers: Primary 16E35, 18G25; Secondary 18G80

Supported by: This work was financially supported by National Natural Science Foundation of China (Grant No.12071120).