Mordell-Weil rank jumps on families of elliptic curves

Abstract: We will present some recent developments around the variation of the Mordell-Weil rank in 1-dimensional families of elliptic curves, by studying them in the guise of elliptic surfaces. We will revisit Néron-Shioda's construction of an infinite family of elliptic curves with rank at least 11 and discuss ways of generalizing it.

algebraic geometrynumber theory

Audience: researchers in the topic

Boston University Number Theory Seminar