Capitulation in abelian extensions of number fields
Volume 179 / 2017
Acta Arithmetica 179 (2017), 201-232
MSC: Primary 11R37; Secondary 11R34.
DOI: 10.4064/aa7857-4-2017
Published online: 14 June 2017
Abstract
This paper studies the kernel and cokernel of the map $j:\mathit{Cl}_K \to \mathit{Cl}_L$ where $L$ is an abelian extension of a number field $K$, $\mathit{Cl}_L$ and $\mathit{Cl}_K$ are their respective ideal class groups and $j$ is induced by the lifting of ideals from $K$ to $L$.
