On capitulation of S-ideals in Zp-extensions

Let k be a finite extension of Q and p a prime number. Let K be a Z(p)-extension of k and S the set of all prime ideals in k which are ramified in K. We denote by A'(infinity), the p-Sylow subgroup of the S-divisor class group of K. We give a criterion for A'(infinity) = 0 which can be applied for general Z(p)-extensions. Further, we especially investigate the criterion for a totally real number field k in which p splits completely. (C) 2001 Academic Press.