Local Gorenstein duality for cochains on spaces
Peer reviewed, Journal article
Published version
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Date
2021Metadata
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- Institutt for matematiske fag [2353]
- Publikasjoner fra CRIStin - NTNU [37221]
Original version
https://doi.org/10.1016/j.jpaa.2020.106495Abstract
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