  We compare two maps that arise in study of the cohomology of number fields
with ramification restricted to a finite set S of primes. One of these maps,
which we call an S-reciprocity map, interpolates the values of cup products in
S-ramified cohomology. In the case of p-ramified cohomology of the pth
cyclotomic field for an odd prime p, we use this to exhibit an intriguing
relationship between particular values of the cup product on cyclotomic
p-units. We then consider higher analogues of the S-reciprocity map and relate
their cokernels to the graded quotients in augmentation filtrations of Iwasawa
modules.
