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401-4116-12L 6 Credits BSC , DR , MSC D-MATH

Lectures on Drinfeld Modules

Lecturers & Examiners: Prof. em. Dr. Richard Pink
VVZ CR n/a

Last Updated: 2026-02-05 15:54:12

Abstract

Drinfeld modules: Basic theory, analytic uniformization, moduli spaces, good/bad/semistable reduction, Tate modules, Galois representations, endomorphism rings, etc.

Content

A central role in the arithmetic of fields of positive characteristic p is played by the Frobenius map x ---> x^p. The theory of Drinfeld modules exploits this map in a systematic fashion. Drinfeld modules of rank 1 can be viewed as analogues of the multiplicative group and are used in the class field theory of global function fields. Drinfeld modules of arbitrary rank possess a rich theory which has many aspects in common with that of elliptic curves, including analytic uniformization, moduli spaces, good/bad/semistable reduction, Tate modules, Galois representations. A full understanding of Drinfeld modules requires some knowledge in the arithmetic of function fields and, for comparison, the arithmetic of elliptic curves, which cannot all be presented in the framework of this course. Relevant results from these areas will be presented only cursorily when they are needed, but a fair amount of the theory can be developed without them.

Resources

Literature

Drinfeld, V. G.: Elliptic modules (Russian), Mat. Sbornik 94 (1974), 594--627, translated in Math. USSR Sbornik 23 (1974), 561--592. Deligne, P., Husemòˆller, D: Survey of Drinfeld modules, Contemp. Math. 67, 1987, 25-91. Goss, D.: Basic structures in function field arithmetic. Springer-Verlag, 1996. Drinfeld modules, modular schemes and applications. Proceedings of the workshop held in Alden-Biesen, September 9¿14, 1996. Edited by E.-U. Gekeler, M. van der Put, M. Reversat and J. Van Geel. World Scientific Publishing Co., Inc., River Edge, NJ, 1997. Thakur, Dinesh S.: Function field arithmetic. World Scientific Publishing Co., Inc., River Edge, NJ, 2004. Further literature will be indicated during the course

Learning Materials (Links)

General Information

Language
English
Levels
BSC , DR , MSC

Examination

Type
session examination
Mode
oral 20 minutes

Course Components

Type Title Time & Place Hours
lecture Lectures on Drinfeld Modules
Starts Tuesdays and Wednesdays at 16:15.
  • Tue 16:00-18:00 (ON LI NE)
  • Wed 16:00-18:00 (ON LI NE)
3 h weekly

Offered In