Good Reduction of Abelian Varieties

The goal of this seminar is to acquaint ourselves with all varieties abelian, and to study their reduction. People interested in participating should contact Renjie Lyu or Wessel Bindt, or just show up at the seminar.

Time and location: Wednesdays at 13:00 in room F3.20, Science park 107

Talks

19-10-16 Renjie Lyu Basics of abelian varieties (rigidity lemma)
26-10-16 Wessel Bindt Theorems of cube and square, projectivity
02-11-16 Rosa Winter Isogenies, p-rank
09-11-16 Harry Smit Picard scheme
16-11-16 Raymond van Bommel Duality Notes
23-11-16 Wessel Bindt Descent, Néron-Severi group, cohomology of line bundles Notes
07-12-16 Zijian Zhou Polarizations, Zarhin's trick Notes
01-02-16 Julian Lyczak Intro to fundamental groups
01-02-17 Renjie Lyu Tate module Notes
08-02-17 Wessel Bindt Chevalley's theorem, Néron models Notes
17-02-17 Erik Visse The Néron-Ogg-Shafarevich criterion (Location: SP107, F2.01, Time: 12:00) Notes, brief supplementary note

Rough outline of the program

Introduction to abelian varieties
Rigidity lemma and applications
Theorems of the cube and square
Isogenies
The Tate module
Duality, étale cohomology, fundamental group
Serre–Tate
Néron models
Something about local fields

References

S. Bosch, W. Lütkebohmert, M. Raynaud. Néron Models. Springer (1990)

G. van der Geer, B. J. J. Moonen. Abelian Varieties. Book draft, available here

B. M. Litjens. Good Reduction of Abelian Varieties. Master's thesis, available here

J. S. Milne. Abelian Varieties. Online notes, available here

D. Mumford. Abelian Varieties. Oxford University Press (1974)

J. P. Serre, J. Tate. Good Reduction of Abelian Varieties in Math. Ann., 88 (1968), No. 3, pp. 492–517