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arXiv · 1708.01213

Local Langlands correspondence in rigid families

Christian Johansson·James Newton·Claus Sorensen
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Abstract

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

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Christian Johansson, James Newton, Claus Sorensen. 2017-08-03. Local Langlands correspondence in rigid families. https://arxiv.org/abs/1708.01213

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