We prove several characterizations of Gorenstein rings in terms of vanishings of derived functors of certain modules or complexes whose scalars are restricted via contracting endomorphisms. These results can be viewed as analogues of results of Kunz (in the case of the Frobenius) and Avramov-Hochster-Iyengar-Yao (in the case of general contracting endomorphisms).

中文翻译：

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使用收缩自同态表征 Gorenstein 环

我们证明了 Gorenstein 环的几个特征，即某些模块或复合体的派生函子的消失，其标量通过收缩自同态受到限制。这些结果可以看作是 Kunz（在 Frobenius 的情况下）和 Avramov-Hochster-Iyengar-Yao（在一般收缩自同态的情况下）的结果的类似物。