Class groups of Kummer extensions via cup products in Galois cohomology

Karl Schaefer, Eric Stubley

We use Galois cohomology to study the $p$-rank of the class group of $\mathbf{Q}(N^{1/p})$, where $N\equiv 1\mathrm{mod}p$ is prime. We prove a partial converse to a theorem of Calega…