Reciprocity maps with restricted ramification

Abstract

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.