Algebra & Number Theory
- Algebra Number Theory
- Volume 3, Number 2 (2009), 209-236.
Chabauty for symmetric powers of curves
Let be a smooth projective absolutely irreducible curve of genus over a number field , and denote its Jacobian by . Let be an integer and denote the -th symmetric power of by . In this paper we adapt the classic Chabauty–Coleman method to study the -rational points of . Suppose that has Mordell–Weil rank at most . We give an explicit and practical criterion for showing that a given subset is in fact equal to .
Algebra Number Theory, Volume 3, Number 2 (2009), 209-236.
Received: 2 April 2008
Revised: 20 January 2009
Accepted: 17 February 2009
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: 11G35: Varieties over global fields [See also 14G25] 14K20: Analytic theory; abelian integrals and differentials 14C20: Divisors, linear systems, invertible sheaves
Siksek, Samir. Chabauty for symmetric powers of curves. Algebra Number Theory 3 (2009), no. 2, 209--236. doi:10.2140/ant.2009.3.209. https://projecteuclid.org/euclid.ant/1513797356