Local Gorenstein duality for cochains on spaces

Barthel, Tobias; Castellana, Natalia; Heard, Drew; Valenzuela, Gabriel

doi:10.1016/j.jpaa.2020.106495

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Local Gorenstein duality for cochains on spaces

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

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

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https://doi.org/10.1016/j.jpaa.2020.106495
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https://doi.org/10.48550/arXiv.2001.02580
(Preprint)

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Barthel-Castellana-Heard-Valenzuela_Local Gorenstein duality for cochains on spaces_2021.pdf
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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: https://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.