The Local Langlands Correspondence for GLn over p-adic Fields
Specialeforsvar: Tim With Berland
TItel: The Local Langlands Correspondence for GLn over p-adic Fields
Abstract: In this thesis, we give some of the essential constructions of Harris and Taylor () and Scholze () in their respective proofs of the local Langlands correspondence over GLn over p-adic fields. To this end, we give the theory of p-divisible groups, in particular their Dieudonn´e theory and the deformation theory of connected p-divisible groups. We develop the necessary representation-theoretic language, and give the proper statements for both sources. The correspondence is constructed and the differences and similarities of the two approaches are discussed. Furthermore, a detailed proof is provided as to how local class field theory realises the local Langlands correspondence for n = 1.
Vejleder: Fabien Pazuki
Censor: Niels Lauritzen, Aarhus Universitet