Seminar on local Langlands correspondence for GL_n

Date: Thursdays at 2pm, Trinity term 2015

Place: room L4, Mathematical Institute, Oxford

Description of the seminar:

We want to follow [Sch] in his proof of the local Langlands correspondence for GL_n. We hope to be able to outline the proof contained in the paper and show major techniques and methods.

References:

[Sch] P. Scholze, "The local Langlands correspondence for GL_n over p-adic fields"

Timetable:

30th April 2015:

Lecture (Konstantin Ardakov): General introduction - goal of the local Langlands correspondence and Section 1 of [Sch].

7th May 2015:

Lecture (Dan Ciubotaru): Preliminaries on representation theory - type theory, Bernstein center, structure of representations on Galois and automorphic side (Bernstein-Zelevinsky classification). Compare with Section 3 of [Sch]

14th May 2015:

Lecture (Netan Dogra): p-divisible groups and their moduli spaces - discuss Section 2 of [Sch] without vanishing cycles. Mention p-divisible groups arising from abelian varieties.

21st May 2015:

Lecture (Ben Green): Shimura varieties and basic facts about them and about abelian varieties. Follow Section 8 of [Sch].

28th May 2015:

Lecture (Przemyslaw Chojecki): Relation between Rapoport-Zink spaces and Shimura varieties - discuss especially Lemma 9.2 of [Sch]; also discuss Theorems 10.2 and 10.5 on automorphic representations and associated Galois representations.

4th June 2015:

Lecture (Konstantin Ardakov): Vanishing cycles - definition and basic facts. Discuss the end of Section 2 of [Sch] together with the definition of functions f_{\tau,h}.

11th June 2015:

Lecture (Przemyslaw Chojecki): More on functions f_{\tau, h}. Definition of the correspondence rec(\pi). Discuss Corollary 10.3 and Section 11 of [Sch].

18th June 2015:

Lecture (Netan Dogra): Bijectivity of the correspondence and loose ends after Sections 12-14 of [Sch].