English
 
User Manual Privacy Policy Disclaimer Contact us
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

Local Gorenstein duality for cochains on spaces

MPS-Authors
/persons/resource/persons234922

Barthel,  Tobias
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons236382

Valenzuela,  Gabriel
Max Planck Institute for Mathematics, Max Planck Society;

External Ressource
Supplementary Material (public)
There is no public supplementary material available
Citation

Barthel, T., Castellana, N., Heard, D., & Valenzuela, G. (2021). Local Gorenstein duality for cochains on spaces. Journal of Pure and Applied Algebra, 225(2): 106495. doi:10.1016/j.jpaa.2020.106495.


Cite as: http://hdl.handle.net/21.11116/0000-0006-E3B7-B
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.