Jordan S. Ellenberg
Published 2010-01-24Version 1
We study the variation of Mordell-Weil ranks in the Jacobians of curves in a pro-p tower over a fixed number field. In particular, we show that under mild conditions the Mordell-Weil rank of a Jacobian in the tower is bounded above by a constant multiple of its dimension. In the case of the tower of Fermat curves, we show that the constant can be taken arbitrarily close to 1. The main result is used in the forthcoming paper of Guillermo Mantilla-Soler on the Mordell-Weil rank of the modular Jacobian J(Np^m).
Specialization of Mordell-Weil ranks of abelian schemes over surfaces to curves
Genus two curves with quaternionic multiplication and modular jacobian
On the growth of Mordell-Weil ranks in $p$-adic Lie extensions
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