On the Iwasawa $\hat{I}»$-invariant of the cyclotomic ${\mathbb{Z}}_2$-extension of a family of real quadratic fields in which $2$ splits

Josué Ávila, Foivos Chnaras

We study Greenberg's conjecture for cyclotomic ${\mathbb{Z}}_2$-extensions of real quadratic fields. Let $K=\mathbb{Q}(\sqrt{pq})$, where $$ p\equiv 1 \mod 8,\qquad q\equiv 9 \mod {1…