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

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

3 Citations (Scopus)

105 Downloads (Pure)

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
Journal	Annales de L'Institut Fourier
Volume	72
Issue number	2
DOIs	https://doi.org/10.5802/aif.3457
Publication status	Published - 2022
Externally published	Yes

Access to Document

10.5802/aif.3457Licence: CC BY-ND

Rank jumps on elliptic surfaces and the Hilbert propertyFinal publisher's version, 1.33 MBLicence: CC BY-ND

Handle.net

Persistent link

Cite this

@article{dfe4f046b1b746cfab626aafc820764c,

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 $1$.",

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

year = "2022",

doi = "10.5802/aif.3457",

language = "English",

volume = "72",

journal = "Annales de L'Institut Fourier",

issn = "0373-0956",

number = "2",

}

TY - JOUR

T1 - Rank jumps on elliptic surfaces and the Hilbert property

AU - Loughran , Daniel

AU - Salgado, Cecília

PY - 2022

Y1 - 2022

N2 - 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 $1$.

AB - 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 $1$.

U2 - 10.5802/aif.3457

DO - 10.5802/aif.3457

M3 - Article

SN - 0373-0956

VL - 72

JO - Annales de L'Institut Fourier

JF - Annales de L'Institut Fourier

IS - 2

ER -

Rank jumps on elliptic surfaces and the Hilbert property

Abstract

Access to Document

Handle.net

Fingerprint

Cite this