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Mathematics, Algebraic Topology
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.
