Local Langlands correspondence, local factors, and zeta integrals in analytic families
نویسندگان
چکیده
منابع مشابه
Local Langlands Correspondence in Rigid Families
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. W...
متن کاملOn the Local Langlands Correspondence
The local Langlands correspondence for GL(n) of a non-Archimedean local field F parametrizes irreducible admissible representations of GL(n, F ) in terms of representations of the Weil-Deligne group WDF of F . The correspondence, whose existence for p-adic fields was proved in joint work of the author with R. Taylor, and then more simply by G. Henniart, is characterized by its preservation of s...
متن کاملLocal 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...
متن کاملAn introduction to the local Langlands correspondence
In these notes, based on my lectures at the FRG workshop on “Characters, Liftings, and Types” at American University in June 2012, I give an introduction to the conjectural Local Langlands Correspondence (LLC), for split semisimple groups over a nonarchimedean local field. This conjecture has been evolving over the past 45 years (with roots going back much further) to the point that today’s sta...
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The cohomology of the Lubin-Tate tower is known to realize the local Langlands correspondence for GL(n) over a nonarchimedean local field. In this article we make progress towards a purely local proof of this fact. To wit, we find a family of formal schemes V such that the generic fiber of V is isomorphic to an open subset of Lubin-Tate space at infinite level, and such that the middle cohomolo...
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2019
ISSN: 0024-6107,1469-7750
DOI: 10.1112/jlms.12285