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We prove the compatibility of local and global Langlands correspondences for$GL_n$ up to semisimplification for the Galois representations constructed byHarris-Lan-Taylor-Thorne and Scholze. More precisely, let $r_p(\pi)$ denote an$n$-dimensional $p$-adic representation of the Galois group of a CM field $F$attached to a regular algebraic cuspidal automorphic representation $\pi$ of$GL_n(\mathbb{A}_F)$. We show that the restriction of $r_p(\pi)$ to thedecomposition group of a place $v\nmid p$ of $F$ corresponds up tosemisimplification to $rec(\pi_v)$, the image of $\pi_v$ under the localLanglands correspondence. Furthermore, we can show that the monodromy of theassociated Weil-Deligne representation of $.r_p(\pi)|_{G_{F_v}}$ is `morenilpotent' than the monodromy of $rec(\pi_v)$.

Local-global compatibility for regular algebraic cuspidal automorphic representation when $\ell \neq p$