Greenberg's conjecture for real quadratic fields and the cyclotomic ${\mathbb{Z}}_2$-extensions

Lorenzo Pagani

Let ${\mathcal{A}}_n$ be the $2$-part of the ideal class group of the $n$-th layer of the cyclotomic ${\mathbb{Z}}_2$-extension of a real quadratic number field $F$. The cardinality of…