Some height conjectures on abelian schemes

Abstract: Motivated by the conjectures of S. Zhang and Zilber–Pink, I would like to formulate three conjectures about height functions on abelian schemes. These conjectures will represent intersections of respectively unlikely, just likely and very likely kinds. The first one is a Bogomolov type conjecture. The second one is about boundedness of height. The third one is related to uniformity of the height bound. Some known results will be mentioned during the talk. I will then discuss an interesting implication: a specialization theorem for the Mordell–Weil group of an elliptic surface of Silverman.

algebraic geometrynumber theory

Audience: researchers in the topic

MIT number theory seminar

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