Seminar on abelian varieties

Seminar on abelian varieties

Semester
SoSe 2017

Lecturer
Prof. Dr. Uwe Jannsen, Dr. Yigeng Zhao

Type of course (Veranstaltungsart)
Seminar

Contents
The aim of this seminar is to learn some basic theory of abelian varieties over a field k, which are one of the most important and most studied objects in arithmetic geometry. Abelian varieties are proper algebraic varieties that carry a group structure, and are a higher dimensional generalization of elliptic curves. In this seminar we follow several references in order to compare the analytic and algebraic tools. More precisely, we will focus on:
(i) basic theorems of abelian varieties, such as: commutativity, projectivity etc.;
(ii) complex torus, line bundles on a complex torus, and the algebraiziability of a complex torus;
(iii) the construction of dual abelian varieties;
(iv) Endomorphisms of abelian varieties.

Literature
D. Mumford: Abelian varieties.

Recommended previous knowledge
Algebraic Geometry I, II

Time/Date
Wednesday 10-12 Uhr

Location
M 009

Course homepage
http://homepages.uni-regensburg.de/~zhy26826/
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration

Organisational meeting/distribution of topics: On 09.02.2017 at 16:00 in M223 or by email:
yigeng.zhao@ur.de
Registration for course work/examination/ECTS: FlexNow

Course work (Studienleistungen)

Presentation: Giving a seminar talk of roughly 90 minutes

Examination (Prüfungsleistungen)

Detailed written report of the seminar talk

Regelungen bei Studienbeginn vor WS 2015 / 16

Benotet:
- O. g. Studienleistung und o. g. Prüfungsleistung; die Note ergibt sich aus dem Seminarvortrag
Unbenotet:

Modules
BSem, MSem

ECTS
Siehe Modulkatalog. MV und Nebenfach: 4,5 LP bei Studienbeginn ab WS 15/16, 6 LP bei Studienbeginn
vor WS 15/16