Conic bundles and Mordell–Weil ranks of elliptic surfaces
Let k be a number field and E an elliptic curve defined over the function field k ( T ) given by an equation of the form y 2 = a 3 x 3 + a 2 x 2 + a 1 x + a 0 , where a i ∈ k [ T ] and deg a i ≤ 2 . We explore the conic bundle structure over the x -line to obtain lower and upper bounds for the Mordell–Weil rank of E ( k ( T ) ) .
Authors
- Felipe Zingali Meira (ORCID: https://orcid.org/0000-0002-9856-5389)
Institutions
- Universidade Federal do Rio de Janeiro (BR)
- Rijksmuseum (NL)
- University of Groningen (NL)
Publication Details
- Journal
- Journal of Number Theory
- Published
- 2025-06-19
- DOI
- https://doi.org/10.1016/j.jnt.2025.05.013
- Primary Topic
- Algebraic Geometry and Number Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Rijksuniversiteit Groningen
- Coordenação de Aperfeiçoamento de Pessoal de Nível Superior