Sur la dualite et la descente d'Iwasawa

TL;DR

This paper develops a formal framework for descent and codescent in Iwasawa theory, showing their equivalence and providing arithmetic applications.

Contribution

It introduces a formalism linking descent and codescent in Iwasawa theory, with new results on their equivalence and practical arithmetic implications.

Findings

Descent and codescent are essentially equivalent in Iwasawa theory.

The formalism applies to arithmetic problems in number theory.

Concrete applications demonstrate the theory's utility.

Abstract

We develop a formalism for studying descent and codescent in the context of Iwasawa theory. The main result essentially states that to control descent or codescent amounts to the same. Arithmetic applications are given.