# Capitulation kernels of class groups over Z_p^d-extensions

## TL;DR

This paper extends Iwasawa's theorem on class groups from $ ext{Z}_p$-extensions to more complex $ ext{Z}_p^d$-extensions, broadening the understanding of class group behavior in number theory.

## Contribution

It introduces a generalization of Iwasawa's theorem applicable to all $ ext{Z}_p^d$-extensions, expanding the scope of class group analysis.

## Key findings

- Generalization of Iwasawa's theorem to $ ext{Z}_p^d$-extensions
- New insights into capitulation kernels in higher-dimensional extensions
- Enhanced understanding of class group structure in complex extensions

## Abstract

We generalize Iwasawa's theorem on class group over $\Z_p$-extensions to all $\Z_p^d$-extensions.