Construction of Zp-extensions with prescribed Iwasawa λ-invariants

It is a basic problem in Iwasawa theory that the existence of a Zp-extension with prescribed Iwasawa invariants. Since the Iwasawa λ-invariant is regarded as an analogue of (twice of) the genus of an algebraic curve, we are especially interested in the problem on the Iwasawa λ-invariants. In this article, for a few prime numbers p, we show that there is a Zp-extension with prescribed Iwasawa λ-invariant by using Kida's formula, which is a number field analogue of the Riemann–Hurwitz formula.