On maximal tamely ramified pro-2-extensions over the cyclotomic $\mathbb{Z}_{2}$-extension of an imaginary quadratic field

Abstract

In [7], Yasushi Mizusawa gives computations which lead to a pro-$2$-presentation of the Galois group of the maximal unramified pro-$2$-extension of the cyclotomic $\mathbb{Z}_{2}$-extension over some imaginary quadratic fields, with low $\lambda$-invariants. We show that these methods can be applied to some maximal tamely ramified pro-$2$-extensions, depending on the quadratic imaginary field, and the condition of ramification.