EVENT DETAILS AND ABSTRACT

Title: Vojta's conjecture and uniform boundedness of full-level structures on abelian varieties over number fields
Speaker: Anthony Várilly-Alvarado
Speaker Info: Rice University
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Abstract:

In 1977, Mazur proved that the torsion subgroup of an elliptic curve over Q is, up to isomorphism, one of only 15 groups. Before Merel gave a qualitative generalization of this result to arbitrary number fields, it was known that variants of the abc conjecture would imply uniform boundedness of torsion on elliptic curves over number fields of bounded degree. In this talk, I will explain how, using Vojta’s conjecture as a higher-dimensional generalization of the abc conjecture, one can deduce similar uniform boundedness statements for full-level structures on abelian varieties of fixed dimension over number fields. This is joint work with Dan Abramovich and Keerthi Madapusi-Pera.