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CATEGORIES:Number Theory Seminar
SUMMARY:On some local-to-global phenomena for abelian vari
eties - Barinder Banwait (Warwick)
DTSTART;TZID=Europe/London:20130226T161500
DTEND;TZID=Europe/London:20130226T171500
UID:TALK42680AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/42680
DESCRIPTION: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 wh
ether the converse of this is true\; in both cases
\, it is not\, as shown by Nick Katz in the torsio
n case\, and Andrew Sutherland for elliptic curves
in the isogeny case. Sutherland had to make a cer
tain assumption about his number field to get his
result\; I have been looking into what happens wit
hout this assumption\, and this leads to lots of i
nteresting 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 m
y attempts at proving that the local-to-global for
torsion holds for certain natural classes of abel
ian varieties.
LOCATION:MR14
CONTACT:Teruyoshi Yoshida
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