On Greenberg’s conjecture for certain real biquadratic fields

Abstract

In this paper, we give the structure of the Iwasawa module \(X=X(k_{\infty })\) of the \(\mathbb {Z}_{2}\)-extension of infinitely many real biquadratic fields k. Denote by \(\lambda , \mu \) and \(\nu \) the Iwasawa invariants of the cyclotomic \(\mathbb {Z}_{2}\)-extension of k. Then \(\lambda =\mu =0 \) and \(\nu =2\).