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Local Gorenstein duality for cochains on spaces. (English) Zbl 07241702
The paper under review develops a homotopical notion of local Gorenstein duality for commutative ring spectra. The main result provides conditions under which a ring spectrum \(R \to k\) has local Gorenstein duality. The method of proof uses an ascent theorem for the local case based on the general Gorenstein ascent of W. G. Dwyer et al. [Adv. Math. 200, No. 2, 357–402 (2006; Zbl 1155.55302)]. A number of examples of the form \(R = C^*(X;k)\) are given, for various spaces \(X\) of interest.
MSC:
55U30 Duality in applied homological algebra and category theory (aspects of algebraic topology)
55R35 Classifying spaces of groups and \(H\)-spaces in algebraic topology
13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
13D45 Local cohomology and commutative rings
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