Elliptic curves, moduli spaces and modular forms II

Elliptic curves, moduli spaces and modular forms II

Semester
SoSe 2022

Lecturer
Guido Kings

Type of course (Veranstaltungsart)
Vorlesung

German title
Elliptische Kurven, Modulräume und Modulformen II

Contents
After the introduction of the necessary notions and techniques from algebraic geometry to study
moduli spaces of elliptic curves in the first part of the course, we will in this second part
define and study the moduli space itself. Important topics will be the algebraic definition of
modular forms and their q-expansion, which involves the construction of the Tate curve. Further we
study elliptic curves over finite fields and Galois representations associated to modular
forms. In the end will define and study p-adic modular forms, which are nowadays an extremely
important tool in number theory and which play an important role in the proof of the
Shimura-Taniyama conjecture by Wiles. People with a very good background in algebraic geometry,
but who have not heard the first part, are still invited to participate.

Literature
Will be announced during the lecture.

Time/Date
Tue and Thu 14 - 16

Location
Tue M101, Thu M102

Course homepage
https://www.uni-regensburg.de/mathematik/mathematik-kings/startseite/index.html
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration

Preliminary registration for the organisation of exercise classes: at the end of the previous
semester via EXA or LSF (see announcement by the department)
Registration for the exercise classes: via GRIPS in the first week of the lecture period
Registration for course work/examination/ECTS: FlexNow

Course work (Studienleistungen)

Successful participation in the exercise classes: 50% of the maximal points in the exercise
sheets

Examination (Prüfungsleistungen)

Oral exam: Duration: 30 minutes, Date: individual, re-exam: Date: individual

Modules
BV, MV, MArGeo, MGAGeo, LA-GyGeo

ECTS
9