Local Gorenstein duality for cochains on spaces
Barthel, Tobias (Max Planck Institute for Mathematics)
Castellana, Natàlia (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Heard, Drew (Norwegian University of Science and Technology. Department of Mathematical Sciences)
Valenzuela, Gabriel (Max Planck Institute for Mathematics)

Date:	2021
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.
Grants:	European Commission 751794 Agencia Estatal de Investigación MTM2016-80439-P Ministerio de Economía y Competitividad MDM-2014-0445
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Gorenstein duality ; Local cohomology ; Structured ring spectra ; p-compact groups ; p-local finite groups
Published in:	Journal of Pure and Applied Algebra, Vol. 225, Num. 2 (February 2021) , art. 106495, ISSN 0022-4049

DOI: 10.1016/j.jpaa.2020.106495

24 p, 463.0 KB

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