Geodesic
On homotopy categories of Gorenstein modules: Compact generation and dimensions
Homology, homotopy, and applications, Tome 17 (2015) no. 2, pp. 13-24.

Voir la notice de l'article provenant de la source International Press of Boston

Let $A$ be a virtually Gorenstein algebra of finite CM-type. We establish a duality between the subcategory of compact objects in the homotopy category of Gorenstein projective left $A$-modules and the bounded Gorenstein derived category of finitely generated right $A$-modules. Let $R$ be a two-sided noetherian ring such that the subcategory of Gorenstein flat modules $R\mbox{-}\mathcal{GF}$ is closed under direct products. We show that the inclusion $K(R\mbox{-}\mathcal{GF})\to K(R\mbox{-}{\rm Mod})$ of homotopy categories admits a right adjoint. We introduce the notion of Gorenstein representation dimension for an algebra of finite CM-type, and give a lower bound by the dimension of its bounded Gorenstein derived category.
DOI : 10.4310/HHA.2015.v17.n2.a2
Classification : 18G25
Keywords: Gorenstein projective module, Gorenstein flat module, compactly generated homotopy category, Gorenstein representation dimension 
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     author = {Nan Gao},
     title = {On homotopy categories of {Gorenstein} modules: {Compact} generation and dimensions},
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     pages = {13--24},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2015.v17.n2.a2/}
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Nan Gao. On homotopy categories of Gorenstein modules: Compact generation and dimensions. Homology, homotopy, and applications, Tome 17 (2015) no. 2, pp. 13-24. doi : 10.4310/HHA.2015.v17.n2.a2. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2015.v17.n2.a2/

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