Iwasawa module of the cyclotomic ${\mathbb{Z}}_2$-extension of certain real quadratic fields

Josue Avila

For a real quadratic field $K=\mathbb{Q}(\sqrt{D})$, let $K_{\infty }$ denote the cyclotomic ${\mathbb{Z}}_p$-extension of $K$. Greenberg conjectured that the corresponding Iwasawa…