THE CLASS GROUP OF Z_p-EXTENSIONS OVER TOTALLY REAL NUMBER FIELDS

Abstract

Let p be an odd prime. We shall give a criterion for p-divisibility of the class number of the n-th layer of a Zp-extension over a certain totally real number field by means of the value of the p-adic zeta function. We shall also discuss the capitulation in such a Zp-extension and a sufficient condition for the Iwasawa λ- and μ-invariants of it to vanish.