Algebra & Number Theory
- Algebra Number Theory
- Volume 5, Number 4 (2011), 465-493.
Specializations of elliptic surfaces, and divisibility in the Mordell–Weil group
Let be an elliptic surface defined over a number field , let be a section, and let be a rational prime. We bound the number of points of low algebraic degree in the -division hull of at the fibre . Specifically, for with such that is nonsingular, we obtain a bound on the number of such that , and such that for some . This bound depends on , , , , and , but is independent of .
Algebra Number Theory, Volume 5, Number 4 (2011), 465-493.
Received: 1 October 2009
Revised: 10 March 2010
Accepted: 21 August 2010
First available in Project Euclid: 21 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11G05: Elliptic curves over global fields [See also 14H52]
Secondary: 14J27: Elliptic surfaces 14G05: Rational points
Ingram, Patrick. Specializations of elliptic surfaces, and divisibility in the Mordell–Weil group. Algebra Number Theory 5 (2011), no. 4, 465--493. doi:10.2140/ant.2011.5.465. https://projecteuclid.org/euclid.ant/1513882223