The unit norm index and $p$-class group in certain degree $\ell$ extensions

Abstract

We examine when units in a field are the norms of elements in an extension field, given certain conditions. We apply these results to the study of the $\ell$-class groups in lifts of the anti-cyclotomic ${\mathbb{Z}}_2$-extension of $\mathbb{Q}(i)$.

24 pages