Abstract We investigate when a commutative ring spectrum R satisfies a homotopical version of local Gorenstein duality, extending the notion previously studied by Greenlees. In order to do this, we prove an ascent theorem for local Gorenstein duality along morphisms of k-algebras. Our main examples are of the form R = C ⁎ ( X ; k ) , the ring spectrum of cochains on a space X for a field k. In particular, we establish local Gorenstein duality in characteristic p for p-compact groups and p-local finite groups as well as for k = Q and X a simply connected space which is Gorenstein in the sense of Dwyer, Greenlees, and Iyengar.

中文翻译：

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空间上 cochains 的局部 Gorenstein 对偶性

摘要 我们研究交换环谱 R 何时满足局部 Gorenstein 对偶的同伦版本，扩展了 Greenlees 先前研究的概念。为了做到这一点，我们沿 k-代数的态射证明了局部 Gorenstein 对偶性的上升定理。我们的主要例子是 R = C ⁎ ( X ; k ) 的形式，即空间 X 上域 k 的辅链的环谱。特别地，我们在特征 p 中为 p 紧群和 p 局部有限群以及 k = Q 和 X 建立了局部 Gorenstein 对偶性，即 Dwyer、Greenlees 和 Iyengar 意义上的 Gorenstein 单连通空间。