Local Langlands Correspondence in Rigid Families
نویسنده
چکیده
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-étale over weight space. More precisely we interpolate the local Langlands correspondence for GLn 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.
منابع مشابه
Local Langlands in Rigid Families
We show that local-global compatibility away from p holds at points on the (p-adic) eigenvariety of a definite unitary group which are étale over weight space. The novelty is we allow non-classical points. More precisely we interpolate the local Langlands correspondence across the eigenvariety by considering the stalks of its defining coherent sheaf. We employ techniques of Scholze from his rec...
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