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401-3119-08L 10 Credits BSC , DR , MSC D-USYS , D-BAUG , D-MAVT , D-INFK , D-MTEC , D-MATH , D-BIOL , D-ERDW , D-GESS , D-ITET , D-CHAB

Modular Curves

Modulkurven

Lecturers & Examiners: Prof. em. Dr. Gisbert Wüstholz
VVZ CR n/a

Last Updated: 2026-02-05 15:29:50

Abstract

Algebraic curves, elliptic curves, moduli problems, Riemann-Roch, SL(2,R) and its discrete subgroups, modular curves, modular forms, Hecke operators

Content

In this course we shall give an introduction to modular curves. These curves are so-called moduli spaces for elliptic curves with additional properties. The extra properties may vary and the outputs are different modular curves. The additional information is encoded in discrete subgroups of SL(2,R). We shall begin with a careful study of elliptic curves, the objects which are classified by modular curves. Then we shall give a crash course into algebraic curves including some some basic aspects of cohomology and the theorem of Riemann-Roch for curves. Then we shall introduce modular curves and study the associated Riemann surfaces. An important object here is the so-called canonical divisor. Its sections are modular forms which will be introduced next. At the end of the course - if time allows - we shall introduce Hecke operators and possibly Hecke correspondences.

General Information

Language
English
Levels
BSC , DR , MSC

Examination

Type
session examination
Mode
oral 30 minutes

Course Components

Type Title Time & Place Hours
lecture Modulkurven
  • Tue 10:15-12:00 (HG F 3)
  • Fri 08:15-10:00 (HG E 3)
4 h weekly
exercise Modulkurven
  • Wed 15:15-16:00 (HG G 26.1)
  • Wed 16:15-17:00 (HG G 26.1)
1 h weekly

Offered In