On $L$-packets and depth for $SL_2(K)$ and its inner form
  We consider the group $SL_2(K)$, where $K$ is a local non-archimedean field of characteristic two. We prove that the depth of any irreducible representation of $SL_2 (K)$ is larger than the depth of the corresponding Langlands parameter, with equality if and only if the L-parameter is essentially tame.   We also work out a classification of all $L$-packets for $SL_2 (K)$ and for its non-split inner form, and we provide explicit formulae for the depths of their $L$-parameters. 
Anne-Marie Aubert, Sergio Mendes, Roger Plymen, Maarten Solleveld
math.RT