In this article we study the interplay between algebro-geometric notions
related to $\pi$-points and structural features of the stable Auslander-Reiten
quiver of a finite group scheme. We show that $\pi$-points give rise to a
number of new invariants of the AR-quiver on one hand, and exploit
combinatorial properties of AR-components to obtain information on $\pi$-points
on the other. Special attention is given to components containing Carlson
modules, constantly supported modules, and endo-trivial modules.