On the Birch-Swinnerton-Dyer conjecture for elliptic curves with complex multiplication

On the Birch-Swinnerton-Dyer conjecture for elliptic curves with
complex multiplication

Semester
WiSe 2023 / 24

Lecturer
Guido Kings

Type of course (Veranstaltungsart)
Vorlesung

German title
Über die Birch-Swinnerton-Dyer Vermutung für elliptische Kurven mit komplexer
Multiplikation

Contents
The Birch-Swinnerton-Dyer conjecture is one of the millennium problems in number theory and still
wide open in general. In the case of elliptic curves with complex multiplication, there is an
approach by Coates and Wiles which is accessible for students with a good knowledge of Algebraic
Number Theory I, II. In this lecture we will present this approach which is based on the study of
formal groups and explicit reciprocity laws, developing all these concepts carefully. Knowledge
about elliptic curves is not necessary.

Time/Date
Di 14-16 und Do 14-16

Location
PHY 5.0.20 (Di), M 103 (Do)

Course homepage
https://elearning.uni-regensburg.de/course/view.php?id=62383
(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 lecure 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
MV, MArGeo, MGAGeo

ECTS
9