Rank jumps on elliptic surfaces and the Hilbert property

Loughran, Daniel; Salgado, Cecília

doi:10.5802/aif.3457

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学術論文

Rank jumps on elliptic surfaces and the Hilbert property

MPS-Authors

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

External Resource

https://doi.org/10.5802/aif.3457
(出版社版)

https://doi.org/10.48550/arXiv.1907.01987
(プレプリント)

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Loughran-Salgado_Rank jumps on elliptic surfaces and the Hilbert property_2022.pdf
(出版社版), 2MB

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引用

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.

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

要旨

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.