Geodesic
Triangulated Equivalences Involving Gorenstein Projective Modules
Canadian mathematical bulletin, Tome 60 (2017) no. 4, pp. 879-890

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DOI

For any ring $R$ , we show that, in the bounded derived category ${{D}^{b}}(\text{Mod}\,R)$ of left $R$ -modules, the subcategory of complexes with finite Gorenstein projective (resp. injective) dimension modulo the subcategory of complexes with finite projective (resp. injective) dimension is equivalent to the stable category $\underline{\text{GP}}(\text{Mod}\,R)\,(resp.\overline{GI}(Mod\,R))$ of Gorenstein projective (resp. injective) modules. As a consequence, we get that if $R$ is a left and right noetherian ring admitting a dualizing complex, then $\underline{\text{GP}}(\text{Mod}\,R)$ and $\overline{\text{GI}}(\text{Mod}\,R)$ are equivalent.
DOI : 10.4153/CMB-2017-045-2
Mots-clés : 18G25, 16E35, triangulated equivalence, Gorenstein projective module, stable category, derived category, homotopy category 
Zheng, Yuefei; Huang, Zhaoyong. Triangulated Equivalences Involving Gorenstein Projective Modules. Canadian mathematical bulletin, Tome 60 (2017) no. 4, pp. 879-890. doi: 10.4153/CMB-2017-045-2
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     author = {Zheng, Yuefei and Huang, Zhaoyong},
     title = {Triangulated {Equivalences} {Involving} {Gorenstein} {Projective} {Modules}},
     journal = {Canadian mathematical bulletin},
     pages = {879--890},
     year = {2017},
     volume = {60},
     number = {4},
     doi = {10.4153/CMB-2017-045-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-045-2/}
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