Algebra & Number Theory
- Algebra Number Theory
- Volume 7, Number 4 (2013), 765-793.
Explicit Chabauty over number fields
Let be a smooth projective absolutely irreducible curve of genus over a number field of degree , and let denote its Jacobian. Let denote the Mordell–Weil rank of . We give an explicit and practical Chabauty-style criterion for showing that a given subset is in fact equal to . This criterion is likely to be successful if . We also show that the only solution to the equation in coprime nonzero integers is . This is achieved by reducing the problem to the determination of -rational points on several genus- curves where or and applying the method of this paper.
Algebra Number Theory, Volume 7, Number 4 (2013), 765-793.
Received: 6 July 2010
Revised: 23 July 2012
Accepted: 31 October 2012
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11G30: Curves of arbitrary genus or genus = 1 over global fields [See also 14H25]
Secondary: 14K20: Analytic theory; abelian integrals and differentials 14C20: Divisors, linear systems, invertible sheaves
Siksek, Samir. Explicit Chabauty over number fields. Algebra Number Theory 7 (2013), no. 4, 765--793. doi:10.2140/ant.2013.7.765. https://projecteuclid.org/euclid.ant/1513729980