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The Local Langlands Correspondence for Tamely Ramified Groups

Posted on:2012-04-20Degree:Ph.DType:Thesis
University:Harvard UniversityCandidate:Roe, David LawrenceFull Text:PDF
GTID:2450390008995646Subject:Mathematics
Abstract/Summary:
This thesis generalizes the work of DeBacker and Reeder [16] to the case of reductive groups splitting over a tame extension of the field of definition. The approach is broadly similar and the restrictions on the parameter the same, but many of the details of the arguments differ.;Let G be a unitary group defined over a local field K and splitting over a tame extension E/K. Given a Langlands parameter ϕ : WK → LG that is tame, discrete and regular, we give a natural construction of an L-packet pi ϕ associated to ϕ, consisting of representations of pure inner forms of G(K) and parameterized by the characters of the finite abelian group Aϕ = Z G(ϕ).
Keywords/Search Tags:Tame
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