Abstract: Let $F$ be a finite extension of $\Q_p$, and let $G$ be a separable, locally profinite group. We consider a smooth $F$-representation $V$ of $G$ obtained by compact induction from an open subgroup that is compact modulo the center. We give a criterion for $V$ to be supercuspidal.  
In the general case, when $V$ is not necessarily supercuspidal, we prove that there exists a finite extension $E/F$ such that $V \otimes_F E$ decomposes as a finite direct sum of absolutely irreducible supercuspidal representations, together with a subrepresentation that contains no $G$-invariant supercuspidal subquotients and no absolutely irreducible admissible $G$-subspaces. These results are analogous to those of Bushnell for complex smooth representations. This is a joint work with David Goldberg. This work is supported in part by the Croatian Science Foundation 

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