  Let F be a non-archimedean local field with residual characteristic p, and k
an algebraically closed field with characteristic l, where l different from p.
Let Rep_k(SL_n(F)) be the category of smooth k-representations of SL_n(F). In
this work, we establish the block decomposition of Rep_k(SL_n(F)) under the
condition that p does not divide the order of the Weyl group of SL_n(F).
