Néron models of Abelian varieties and applications
Student No.:50
Time:Wed. 14:00-16:00 and Fri. 9:30 - 11:30 from Apr. 11 to 27; 9:30 - 11:30 on Apr. 23 and May 7
Instructor:Qing Liu  [Université Bordeaux 1]
Place:Conference Room 1, Floor 1, Jin Chun Yuan West Building
Starting Date:2012-4-11
Ending Date:2012-5-7

Course description:

Important arithmetic properties and numerical invariants of Abelian varieties over number fields are encoded in their Néron models (reduction type, conductor, Tamagawa number etc). The Néron model of an Abelian varitey A is a smooth group scheme over the ring of integers extending A.

The aim of this course is to give a survey on the construction, general properties and known results on Néron models. We will also consider the special cases of elliptic curves and more generally of Jacobians with some concrete computations.



Reasonable background in algebraic geometry (in the language of schemes) is needed. Knowledges in groups schemes and basic notion on Abelian varieties are welcome.


Reference for the course:

     R. Hartshorne: Algebraic geometry, chapters II, III
     Q. Liu: Algebraic geometry and Arithmetic curves, chapters II-VI.

Abelian varieties:
     J. Milne: Abelian varieties,

Néron models:
     S. Bosch, W. Lütkebohmert and M. Raynaud, Néron models
     M. Artin: Néron models, in “Arithmetic geometry” (Cornell and Silverman)