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.