  We strengthen the local-global compatibility of Langlands correspondences for
$GL_{n}$ in the case when $n$ is even and $l\not=p$. Let $L$ be a CM field and
$\Pi$ be a cuspidal automorphic representation of $GL_{n}(\mathbb{A}_{L})$
which is conjugate self-dual. Assume that $\Pi_{\infty}$ is cohomological and
not "slightly regular", as defined by Shin. In this case, Chenevier and Harris
constructed an $l$-adic Galois representation $R_{l}(\Pi)$ and proved the
local-global compatibility up to semisimplification at primes $v$ not dividing
$l$. We extend this compatibility by showing that the Frobenius
semisimplification of the restriction of $R_{l}(\Pi)$ to the decomposition
group at $v$ corresponds to the image of $\Pi_{v}$ via the local Langlands
correspondence. We follow the strategy of Taylor-Yoshida, where it was assumed
that $\Pi$ is square-integrable at a finite place. To make the argument work,
we study the action of the monodromy operator $N$ on the complex of nearby
cycles on a scheme which is locally etale over a product of semistable schemes
and derive a generalization of the weight-spectral sequence in this case. We
also prove the Ramanujan-Petersson conjecture for $\Pi$ as above.
