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Let F be a non-archimedean local field with residual characteristic p, and kan 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). Inthis work, we establish the block decomposition of Rep_k(SL_n(F)) under thecondition that p does not divide the order of the Weyl group of SL_n(F).

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