On some local-to-global phenomena for abelian varieties

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• Barinder Banwait (Warwick)
• Tuesday 26 February 2013, 16:15-17:15
• MR14.

If you have a question about this talk, please contact Teruyoshi Yoshida.

If an abelian variety over a number field admits a rational torsion point, or isogeny, then so too do (almost) all of its reductions. One may ask whether the converse of this is true; in both cases, it is not, as shown by Nick Katz in the torsion case, and Andrew Sutherland for elliptic curves in the isogeny case. Sutherland had to make a certain assumption about his number field to get his result; I have been looking into what happens without this assumption, and this leads to lots of interesting questions about the image of the mod-l representation attached to elliptic curves, which can be studied by explicitly constructing certain modular curves. If there’s time I’ll talk about my attempts at proving that the local-to-global for torsion holds for certain natural classes of abelian varieties.

This talk is part of the Number Theory Seminar series.

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