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A Deuring criterion for abelian varieties

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  • UserChris Blake (Cambridge)
  • ClockTuesday 19 November 2013, 16:15-17:15
  • HouseMR13.

If you have a question about this talk, please contact James Newton.

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 prove several generalisations of the Deuring reduction criterion to abelian varieties of arbitrary dimension.

This talk is part of the Number Theory Seminar series.

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