Towards the global Langlands correspondence over function fields
Towards the global Langlands correspondence over function fields
Winter term 2023/2024
News:
The lecture on 14.12. takes place in room C01-136.
The exercise class on 21.11. is cancelled.
The lecture on 16.11. is moved to Wednesday, 15.11., 14:15, in room U2-200.
There has been a room change: The lecture takes place in V2-210 (instead of V5-148) on Thursdays.
General information:
Lecture: Thu, 10-12, V2-210 (starting October 12)
Discussion/Exercise session: Tue, 16-18, T2-220 (starting October 10)
Content:
Moduli spaces of shtukas serve as analogues of Shimura varieties over function fields of positive characteristic. They are used with great success in the construction of a global Langlands correspondence for reductive groups by V. Lafforgue.
In the first part of the course I will introduce moduli spaces of shtukas (and related objects like Drinfeld modular varieties) and explain how they are function field analogues of Shimura varieties. We then continue to look at automorphic representations in particular in the function field setting.
In the last part I want to explain some of the ideas that go into Lafforgue's construction - at least in the GL_n-case.
Literature:
For the first part of the course I will roughly follow notes by J. Weinstein, and for the latter part notes taken by T. Feng during a course given by Z. Yun.
Further references are:
V. Lafforgue, Chtoucas pour les groupes réductifs et paramétrisation de Langlands globale, JAMS, 2018, 2018 (31), pp. 719-891, [link]
V. Lafforgue, Shtukas for reductive groups and Langlands correspondence for function fields, Proceedings of the ICM 2018
J.Heinloth, Langlands Parametrization over Function Fields Following V. Lafforgue, Acta Mathematica Vietnamica, 43, 45-66 (2018), [link]
T. Lehmkuhl, Compactifications of Drinfeld modular varieties
G. Laumon, Cohomology of Drinfeld modular varieties. Parts 1 + 2
J. Getz, H.Hahn, An Introduction to Automorphic Representations
V. Drinfeld's papers, in particular: Elliptic modules and Varieties of modules of F-sheaves