# Blocks for mod $p$ representations of $GL 2(Q p)$

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Let $\pi 1$ and $\pi 2$ be absolutely irreducible smooth representations of $G=GL 2(Q p)$ with a central character, defined over a finite field of characteristic $p$. We show that if there exists a non-split extension between $\pi 1$ and $\pi 2$ then they both appear as subquotients of the reduction modulo $p$ of a unit ball in a crystalline Banach