Joint IAS/Princeton University Number Theory Seminar | |

Topic: | On the spectrum of Faltings' height |

Speaker: | Juan Rivera-Letelier |

Affiliation: | University of Rochester |

Date: | Thursday, December 15 |

Time/Room: | 4:30pm - 5:30pm/Fine 214, Princeton University |

The arithmetic complexity of an elliptic curve defined over a number field is naturally quantified by the (stable) Faltings height. Faltings' spectrum is the set of all possible Faltings' heights. The corresponding spectrum for the Weil height on a projective space and the Neron-Tate height of an Abelian variety is dense on a semi-infinite interval. We show that, in contrast, Faltings' height has 2 isolated minima. We also determine the essential minimum of Faltings' height up to 5 decimal places. This is a joint work with Jose Burgos-Gil and Ricardo Menares.