The present state of the capitulation problem

TL;DR

This paper reviews the current understanding of the capitulation problem for class groups of number fields, providing a synthetic overview before Suzuki's proof of the main conjecture.

Contribution

It offers a comprehensive synthesis of the state of knowledge on capitulation in class groups prior to Suzuki's breakthrough.

Findings

Summarizes key results and open questions in capitulation theory.

Highlights the significance of Suzuki's forthcoming proof.

Provides context for future research directions.

Abstract

The text is a synthetic presentation of the state of the knowledge about the capitulation for the class-groups of numbers fields, shortly before the demonstration by Suzuki of the main conjecture on this question.