l-modular blocks of Rep_k(SL_n(F))

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).