  This text takes, with more details and simplifying a proof in section 3, the
parts of [Laf08] and [Laf09] treating p-adic groups. We prove that $SL_{3}$
over a non archimedian local field $F$ has strong Banach property (T). The
applications are as follows: any connected almost $F$-simple algebraic group
$G$ over $F$ whose Lie algebra contains $sl_3(F)$ has strong Banach property
(T), the family of expanders constructed from a lattice of $G(F)$ do not embed
uniformly in any Banach space of type $>1,$ and any isometric affine action of
$G(F)$ on a Banach space of type $>1$ admits a fix point.
