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Let G be a reductive group, defined over the Galois field $${\mathbb{F}_p}$$ with p being good for G. Using support varieties and covering techniques based on G  r  T-modules, we determine the position of simple modules and baby Verma modules within the stable Auslander–Reiten quiver Γ s (G  r ) of the rth Frobenius kernel of G. In particular, we show that the almost split sequences terminating in these modules usually have an indecomposable middle term. Concerning support varieties, we introduce a reduction technique leading to isomorphisms    $$\mathcal{V}_{G_r}(Z_r(\lambda)) \cong \mathcal{V}_{G_{r-d}}(Z_{r-d}(\mu))$$    for baby Verma modules of certain highest weights $${\lambda, \mu \in X(T)}$$, which are related by the notion of depth.

Support varieties, AR-components, and good filtrations