On the Burde--de Rham theorem for finitely presented pro-$p$ groups

Abstract

We consider the Burde--de Rham theorem for finitely presented pro-$p$ groups under the assumption that the total degrees of all relators are $0$. We also give some concrete examples including higher-dimensional cases under Iwasawa theoretic conditions, and consider some cohomological interpretations.

20 pages, to appear in Int. Math. Res. Not. IMRN