Algebra & Number Theory

Chabauty for symmetric powers of curves

Samir Siksek

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Abstract

Let C be a smooth projective absolutely irreducible curve of genus g2 over a number field K, and denote its Jacobian by J. Let d1 be an integer and denote the d-th symmetric power of C by C(d). In this paper we adapt the classic Chabauty–Coleman method to study the K-rational points of C(d). Suppose that J(K) has Mordell–Weil rank at most gd. We give an explicit and practical criterion for showing that a given subset C(d)(K) is in fact equal to C(d)(K).

Article information

Source
Algebra Number Theory, Volume 3, Number 2 (2009), 209-236.

Dates
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
https://projecteuclid.org/euclid.ant/1513797356

Digital Object Identifier
doi:10.2140/ant.2009.3.209

Mathematical Reviews number (MathSciNet)
MR2491943

Zentralblatt MATH identifier
1254.11065

Subjects
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

Keywords
Chabauty Coleman curves Jacobians symmetric powers divisors differentials abelian integrals

Citation

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


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