A spectral sequence for Iwasawa adjoints

TL;DR

This paper introduces an algebraic spectral sequence that connects Iwasawa adjoints of modules in p-adic Lie extensions to Galois cohomology, providing a new tool for number theory research.

Contribution

It develops a novel algebraic spectral sequence linking Iwasawa adjoints with Galois cohomology in p-adic Lie extensions, enhancing analytical methods.

Findings

Establishment of a new spectral sequence relating Iwasawa adjoints and Galois cohomology.

Application of the spectral sequence to natural Iwasawa modules.

Potential for deeper understanding of p-adic Lie extension structures.

Abstract

We establish a purely algebraic tool for studying the Iwasawa adjoints of some natural Iwasawa modules for $p$-adic Lie group extensions of number fields, by relating them to certain continuous Galois cohomology groups via a spectral sequence.