Local Langlands correspondence in rigid families

Christian Johansson; James John Michael Newton; Claus Sorensen

doi:10.2140/pjm.2020.304.65

Local Langlands correspondence in rigid families

Christian Johansson, James John Michael 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. We do this by interpolating the local Langlands correspondence for GL(n) across the eigenvariety by considering the fibers of itsdefining coherent sheaf. We employ techniques of Chenevier and Scholze used in Scholze’s proof of the local Langlands conjecture for GL(n).

Original language	English
Pages (from-to)	65-102
Number of pages	38
Journal	Pacific Journal of Mathematics
Volume	304
Issue number	1
DOIs	https://doi.org/10.2140/pjm.2020.304.65
Publication status	Published - 2020

Keywords

Eigenvarieties
Galois representations
Local langlands correspondence.
P-adic automorphic forms

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10.2140/pjm.2020.304.65

Local Langlands correspondence in rigid_JOHANSSON_Accepted 2 August 2019_GREEN AAMAccepted author manuscript, 547 KB

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KW - Eigenvarieties

KW - Galois representations

KW - Local langlands correspondence.

KW - P-adic automorphic forms

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Local Langlands correspondence in rigid families

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Keywords

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