On the Iwasawa algebra for pro-l Galois groups

TL;DR

This paper provides a detailed algebraic analysis of the Iwasawa algebra associated with pro-l Galois groups over totally real number fields, including structure, cohomology, and completion properties.

Contribution

It offers a comprehensive description of the algebraic structure of the Iwasawa algebra for pro-l Galois groups, extending understanding of its semisimple algebra components.

Findings

Full description of the algebraic structure of QG for pro-l Galois groups

Computed the cohomological dimension of the centers of Wedderburn components

Results on the completion of the Iwasawa algebra QG

Abstract

Let l be an odd prime and K/k a Galois extension of totally real number fields with Galois group G such that K/k_\infty and k/Q are finite. We give a full description of the algebraic structure of the semisimple algebra QG=Quot(\Lambda G) for pro-l Galois groups G with \Lambda G = Z_l[[G]] the Iwasawa algebra. We moreover compute the cohomological dimension of the centres of the Wedderburn components of QG and state some results on the completion of QG.