Congruences between abelian pseudomeasures

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.