Number Theory Seminar

Speaker: Jerson Caro (Boston)

Title: Lower bounds for the Mordell-Weil rank

Abstract: In 1922, Mordell proved that the set of rational points of an elliptic curve defined over the rational numbers is a finitely generated abelian group. This implies that it has finite rank, known as the Mordell-Weil rank.

Obtaining lower bounds for the Mordell-Weil rank of an elliptic curve defined over Q is a relevant problem in number theory. For example, the question of whether the ranks of elliptic curves over Q are uniformly bounded or not remains open due to the lack of sharp bounds.

In this talk, I will present two distinct methods for finding lower bounds. The first method is based on a result by Silverman concerning families of elliptic curves. The second method is based on results of Gao, Ge & Kühne about subvarieties of abelian varieties. This is joint work with N. Garcia-Fritz and H. Pasten.

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