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We complete the results of a previous article. Let $G$ be a split connectedreductive group over a finite extension $F$ of $\mathbb{Q}_p$. When$F=\mathbb{Q}_p$, we determine the extensions between unitary continuous$p$-adic and smooth mod $p$ principal series of $G(\mathbb{Q}_p)$ withoutassuming the centre of $G$ connected nor the derived group of $G$ simplyconnected. This shows a new phenomenon: there may exist several non-isomorphicnon-split extensions between two distinct principal series. We also completethe computations of self-extensions of a principal series in the non-genericcases when the centre of $G$ is connected. Finally, we determine the extensionsof a principal series of $G(F)$ by an "ordinary" representation of $G(F)$ (i.e.parabolically induced from a special representation twisted by a character). Inorder to do so, we compute Emerton's $\delta$-functor $\mathrm{H^\bulletOrd}_{B(F)}$ of derived ordinary parts with respect to a Borel subgroup on anordinary representation of $G(F)$.

Complements sur les extensions entre series principales p-adiques et modulo p de G(F)