A Deuring criterion for abelian varieties
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If you have a question about this talk, please contact Julian Brough.
Let A be an abelian variety defined over a number field with
complex multiplication by a CM field F. If A is an elliptic curve, a famous
criterion of Deuring provides a direct link between the splitting of a
prime number p in F and the reduction type of A at any prime of good
reduction above p. With a bit of thought, it is easy to see that there can
be no such simple relationship as soon as the dimension of A is greater
than 1. Nonetheless, in this talk we will describe several generalisations
of the Deuring reduction criterion to abelian varieties of arbitrary
dimension.
This talk is part of the Junior Algebra and Number Theory seminar series.
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