Rank jumps on elliptic surfaces and the Hilbert property

Daniel Loughran, Cecília Salgado

Research output: Contribution to journalArticlepeer-review

2 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 languageEnglish
Pages (from-to)617-638
Number of pages22
JournalAnnales de l'institut Fourier
Volume72
Issue number2
Early online date7 Jul 2022
DOIs
Publication statusPublished - 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

Fingerprint

Dive into the research topics of 'Rank jumps on elliptic surfaces and the Hilbert property'. Together they form a unique fingerprint.

Cite this