an:07241702
Zbl 1451.55007
Barthel, Tobias; Castellana, Nat??lia; Heard, Drew; Valenzuela, Gabriel
Local Gorenstein duality for cochains on spaces
EN
J. Pure Appl. Algebra 225, No. 2, Article ID 106495, 23 p. (2021).
00452514
2021
j
55U30 55R35 13H10 13D45
Gorenstein duality; local cohomology; structured ring spectra; \(p\)-compact groups; \(p\)-local finite groups
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 \textit{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.
Niles Johnson (Newark)
Zbl 1155.55302