Congruences between abelian pseudomeasures

TL;DR

This paper proves torsion congruences in abelian pseudomeasures, linking them to the main conjecture of equivariant Iwasawa theory and reducing it to the integrality of a specific pseudomeasure.

Contribution

It establishes the validity of torsion congruences in abelian pseudomeasures, advancing the understanding of the main conjecture in equivariant Iwasawa theory.

Findings

Proves torsion congruences for abelian pseudomeasures

Reduces the main conjecture to the integrality of the logarithmic pseudomeasure

Builds on foundational work by Deligne and Ribet

Abstract

Following Deligne and Ribet (`Values of abelian $L$-functions at negative integers over totally real fields.' Invent. Math. 59 (1980), 227-286) we prove that the `torsion congruences' (as introduced in our paper `Non-abelian pseudomeasures and congruences between abelian Iwasawa $L$-functions.' To appear in Pure and Applied Mathematics Quarterly) hold and so reduce the `main conjecture' of equivariant Iwasawa theory to the integrality of the logarithmic pseudomeasure.