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 to deal with certain elusive families.

algebraic geometrynumber theory

Audience: researchers in the topic

MIT number theory seminar

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