Poster Session

We highly encourage participants to contribute posters presenting their research interests, even if they have no original results yet. Making a poster can be a good experience in the preparation of academic materials and provides a vehicle for discussing your work with potential collegues. We will display poster titles and abstracts on this page before the school. We will also display the posters themselves on this page during and after the school. A LaTeX template is available here and a sample poster is available here. For inspiration, the full source for the sample poster is available here. Participants should print their posters on A0 paper at their own expense. If you wish to submit a poster, please let us know as soon as possible.

Stefen Keil, Ш(A/K) of non-square order

Let A be an abelian variety over a number field K and assume that its Tate-Shafarevich group Ш(A/K) is finite. Then the order of Ш(A/K) is a square, if A is an elliptic curve, and is a square or twice a square if A is principally polarized (and both cases occur). Also it seems very likely that if one ranges over all abelian varieties over all number fields then every square-free natural number can appear as the non-square part of the order of Ш(A/K). So the natural question is what are the possible non-square parts of the order of Ш for abelian varieties of fixed dimension over a fixed number field? Is this a finite list? I am especially interested in abelian surfaces S over Q and for the moment I am trying to construct an example where #Ш(S/Q)=5*\square.

Simon Keicher, Computations with Mori dream spaces