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

Voir la notice de l'article provenant de la source Cambridge University Press

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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