  This paper is Part III of the series of work by the first named author on
duality theories for p-primary etale cohomology, whose Parts I and II were
published in 1986 and 1987, respectively. In this Part III, we study a duality
for p-primary etale nearby cycles on smooth schemes over henselian discrete
valuation rings of mixed characteristic (0, p) whose residue field is not
necessarily perfect.
