Local Gorenstein duality for cochains on spaces

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 th...

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Detalles Bibliográficos
Autores: Barthel, Tobias, Castellana, Natàlia|||0000-0003-2839-2002, Heard, Drew|||0000-0002-0895-3354, Valenzuela, Gabriel|||0000-0001-6821-3107
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:324883
Acceso en línea:https://ddd.uab.cat/record/324883
https://dx.doi.org/urn:doi:10.1016/j.jpaa.2020.106495
Access Level:acceso abierto
Palabra clave:Gorenstein duality
Local cohomology
Structured ring spectra
p-compact groups
p-local finite groups
Descripción
Sumario: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.