Joint IAS/PU Number Theory Seminar | |

Topic: | Abelian varieties with maximal Galois action on their torsion points |

Speaker: | David Zywina |

Affiliation: | Queen's University; Member, School of Mathematics |

Date: | Thursday, January 24 |

Time/Room: | 4:30pm - 5:30pm/S-101 |

Video Link: | https://video.ias.edu/1213/jointiaspu/0124-DavidZywina |

Abstract: Associated to an abelian variety A/K is a Galois representation which describes the action of the absolute Galois group of K on the torsion points of A. In this talk, we shall describe how large the image of this representation can be (in terms of a number field K and the dimension of A). We achieve this by considering abelian varieties in families and then using a special variant of Hilbert's irreducibility theorem. Some results of Serre on the mod ell Galois image will also be reviewed. (This is joint work with David Zureick-Brown)