Work

Conic bundles and Mordell–Weil ranks of elliptic surfaces

Year: 2025

Type: article

Abstract: 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 ) ) .

Source: Journal of Number Theory

DOI: 10.1016/j.jnt.2025.05.013

Author: Felipe Zingali Meira

Institutions: Universidade Federal do Rio de Janeiro, University of Groningen

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: Rijksuniversiteit Groningen, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior