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We show that local-global compatibility (at split primes) away from $p$ holdsat all points of the $p$-adic eigenvariety of a definite $n$-variable unitarygroup. The novelty is we allow non-classical points, possibly non-\'{e}taleover weight space. More precisely we interpolate the local Langlandscorrespondence for GL(n) across the eigenvariety by considering the fibers ofits defining coherent sheaf. We employ techniques of Scholze from his newapproach to the local Langlands conjecture.

Local Langlands correspondence in rigid families