Ausoni–Bökstedt duality for topological Hochschild homology

Abstract

We consider the Gorenstein condition for topological Hochschild homology, and show that it holds remarkably often [7]. More precisely, if R is a commutative ring spectrum and R⟶k is a map to a field of characteristic p then, provided k is small as an R-module, THH(R;k) is Gorenstein in the sense of [11]. In particular, this holds if R is a (conventional) regular local ring with residue field k of characteristic p.Using only Bökstedt's calculation of THH(k), this gives a non-calculational proof of dualities visible in calculations of Bökstedt [9], Ausoni [3], Lindenstrauss and Madsen [17], Angeltveit and Rognes [2] and others.