Rank jumps on elliptic surfaces and the Hilbert property

Loughran, Daniel; Salgado, Cecília

doi:10.5802/aif.3457

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Rank jumps on elliptic surfaces and the Hilbert property

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Salgado, Cecília
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.5802/aif.3457
(Publisher version)

https://doi.org/10.48550/arXiv.1907.01987
(Preprint)

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Loughran-Salgado_Rank jumps on elliptic surfaces and the Hilbert property_2022.pdf
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Citation

Loughran, D., & Salgado, C. (2022). Rank jumps on elliptic surfaces and the Hilbert property. Annales de l'Institut Fourier, 72(2), 617-638. doi:10.5802/aif.3457.

Cite as: https://hdl.handle.net/21.11116/0000-000A-D1BB-7

Abstract

Given an elliptic surface over a number field, we study the collection of
fibres whose Mordell-Weil rank is greater than the generic rank. Under suitable
assumptions, we show that this collection is not thin. Our results apply to
quadratic twist families and del Pezzo surfaces of degree 1.