Stefan Keil

Current Position
Since fall 2010, I am a PhD student at
Institut für Mathematik,
Humboldt-Universität zu Berlin.

I am a member of the algebraic geometry group
and my advisor is Prof. Kloosterman.

Currently I am working as a research assistant at the algebraic geometrie group at Leibniz Universität Hannover.

I am supported by the Berlin Mathematical School,
where I contributed in 2012 as a Student Representative.
As part of this, I was in the organizing committee of the
first-ever BMS Student Conference, held after the BMS Days 2013.

Contact Information
Email: [lastname] at math dot hu-berlin dot de
Telephone: +49 (0)30 2093 1816
Fax: +49 (0)30 2093 5853
Office: Room 1.424
Rudower Chaussee 25,
12489 Berlin

Mailing address
Humboldt-Universität zu Berlin
Institut für Mathematik
Unter den Linden 6
D-10099 Berlin
Germany

Research Interests

My research interests lie in the field of arithmetic geometry. Currently I am trying to better understand the arithmetic of abelian varieties over number fields. I am especially interested in the Tate-Shafarevich groups of abelian surfaces over the rationals.
The Tate-Shafarevich groups of elliptic curves have order a perfect square, if the cardinality is finite. This is no longer true in higher dimensions, but for principally polarized abelian varieties only the exceptional case of Tate-Shafarevich groups of order twice a square occurs. I try to figure out what non-square cases can appear in case of non-principally polarized abelian surfaces over the rationals. Before I started, only the exceptional primes 2 and 3 were known. So far, I extended this list by 5 and 7. One expects the list of exceptional primes to be finite for abelian varieties over the rationals of bounded dimension, but one also expects that any prime can appear if the dimension is unbounded.