Rank jumps on elliptic surfaces and the Hilbert property

Daniel Loughran; Cecília Salgado

doi:10.5802/aif.3457

Rank jumps on elliptic surfaces and the Hilbert property

Daniel Loughran, Cecília Salgado

Department of Mathematical Sciences

Rijksuniversiteit Groningen

Research output: Contribution to journal › Article › peer-review

3 Citations (SciVal)

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.

Original language	English
Pages (from-to)	617-638
Number of pages	22
Journal	Annales de l'institut Fourier
Volume	72
Issue number	2
Early online date	7 Jul 2022
DOIs	https://doi.org/10.5802/aif.3457
Publication status	Published - 31 Dec 2022

Bibliographical note

Funding Information:
The first-named author is supported by EPSRC grant EP/R021422/2. The secondnamed author is partially supported by FAPERJ grant E-26/203.205/2016, the Serrapilheira Institute (grant number Serra-1709-17759) and the Capes-Humboldt program.

Funding Information:
(*) The first-named author is supported by EPSRC grant EP/R021422/2. The second-named author is partially supported by FAPERJ grant E-26/203.205/2016, the Serrapil-heira Institute (grant number Serra-1709-17759) and the Capes–Humboldt program.

Keywords

elliptic surfaces
rank jumps
thin sets

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology

Access to Document

10.5802/aif.3457Licence: CC BY-NC-ND

Cite this

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title = "Rank jumps on elliptic surfaces and the Hilbert property",

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.",

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author = "Daniel Loughran and Cec{\'i}lia Salgado",

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language = "English",

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AU - Salgado, Cecília

N1 - Funding Information: The first-named author is supported by EPSRC grant EP/R021422/2. The secondnamed author is partially supported by FAPERJ grant E-26/203.205/2016, the Serrapilheira Institute (grant number Serra-1709-17759) and the Capes-Humboldt program. Funding Information: (*) The first-named author is supported by EPSRC grant EP/R021422/2. The second-named author is partially supported by FAPERJ grant E-26/203.205/2016, the Serrapil-heira Institute (grant number Serra-1709-17759) and the Capes–Humboldt program.

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KW - thin sets

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Rank jumps on elliptic surfaces and the Hilbert property

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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Quantitative arithmetic geometry

Cite this

Rank jumps on elliptic surfaces and the Hilbert property

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Embargoed Document

Fingerprint

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Quantitative arithmetic geometry

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