For more information about this meeting, contact Robert Vaughan, Mihran Papikian.

Title: | Canonical subgroups for abelian varieties |

Seminar: | Algebra and Number Theory Seminar |

Speaker: | Joe Rabinoff, Harvard University |

Abstract: |

An elliptic curve over the integer ring of a p-adic field whose special fiber is ordinary has a canonical line contained in its p-torsion. This fact has many arithmetic applications: for instance, it shows that there is a canonical partially-defined section of the natural map of modular curves X_0(Np) -> X_0(N). Lubin was the first to notice that elliptic curves with "not too
supersingular" reduction also contain a canonical order-p subgroup. I'll begin the talk by giving an overview of Lubin and Katz's theory of the canonical subgroup of an elliptic curve. I'll then explain one approach to defining the canonical subgroup of a general abelian variety (and even p-divisible group), and state a very general existence result. |

### Room Reservation Information

Room Number: | MB315 |

Date: | 04 / 29 / 2010 |

Time: | 02:30pm - 03:20pm |