青年学术论坛邀请报告一（非通俗）

摘要：pdf文件见 （http://math.ecnu.edu.cn/~rdu/forum.htm）

Let $(\mathcal{X}, \mathcal{Z}, \mathcal{Y})$ be a cotorsion triple in an abelian category $\mathcal{A}$. By studying abelian models structures on the category of complexes $\mathrm{Ch}(\mathcal{A})$ induced by $(\mathcal{X}, \mathcal{Z}, \mathcal{Y})$, we obtain equivalences and recollements of homotopy categories. As an application, we prove that for a left-Gorenstein ring, there exist equivalences $\mathrm{D}_{\mathcal{G}(\mathcal{PI})}^{sing}(R):= \mathrm{K}_{ex}(\mathcal{GP})\cong \mathrm{K}_{ex}(\mathcal{GI})$ and $\mathrm{D}_{\mathcal{G}(\mathcal{PI})}(R):= \mathrm{K}(\mathcal{GP})\cong \mathrm{K}(\mathcal{GI})$, between the homotopy categories of (exact) complexes of Gorenstein projective and Gorenstein injective modules, and then there is a recollement
\[\text{D}_{\mathcal{G}(\mathcal{P}\mathcal{I})}^{sing}(R)\underset{{}}\leftrightarrow{{}}{{\text{D}}_{\mathcal{G}(\mathcal{P}\mathcal{I})}}(R)\underset{{}}\leftrightarrow {{}}\text{D}(R)\]Moreover, these restrict to equivalences and a recollement for homotopy categories with respect to projective and injective modules.

邀请人：周国栋