JOINT IAS/PU NUMBER THEORY SEMINAR | |

Topic: | Split Reductions of Simple Abelian Varieties |

Speaker: | David Zywina |

Affiliation: | University of Pennsylvania |

Date: | Thursday, April 15 |

Time/Room: | 4:30pm - 5:30pm/Fine Hall -- 214 |

To an abelian variety over a number field one can associate an abelian variety to each prime ideal p of good reduction by reducing the variety modulo p . The geometry of these reductions need not resemble the geometry of the original abelian variety; for example, there are absolutely simple abelian varieties of dimension 2 whose reductions modulo p always split as a product of elliptic curves. In this talk, we shall describe progress on a conjecture of Murty and Patankar which predicts exactly which absolutely simple abelian varieties have reductions modulo p that are also absolutely simple.