On the catenarity of virtually nilpotent mod-$p$ Iwasawa algebras

Abstract

Let $p>2$ be a prime, $k$ a finite field of characteristic $p$, and $G$ a nilpotent-by-finite compact $p$-adic analytic group. Write $kG$ for the completed group ring of $G$ over $k$. We show that $kG$ is a catenary ring.