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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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