Standard Hausdorff spectrum of compact ${\mathbb{F}}_p[[t]]$-analytic groups

Abstract

We prove that the ${\mathbb{F}}_p[[t]]$-standard Hausdorff spectrum of a compact ${\mathbb{F}}_p[[t]]$-analytic group contains a real interval and that it coincides with the full unit interval when the group is soluble. Moreover, we show that the ${\mathbb{F}}_p[[t]]$-standard Hausdorff spectrum of classical Chevalley groups over ${\mathbb{F}}_p[[t]]$ is not full, since 1 is an isolated point thereof.