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2009 Chabauty for symmetric powers of curves
Samir Siksek
Algebra Number Theory 3(2): 209-236 (2009). DOI: 10.2140/ant.2009.3.209

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).

Citation

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Samir Siksek. "Chabauty for symmetric powers of curves." Algebra Number Theory 3 (2) 209 - 236, 2009. https://doi.org/10.2140/ant.2009.3.209

Information

Received: 2 April 2008; Revised: 20 January 2009; Accepted: 17 February 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1254.11065
MathSciNet: MR2491943
Digital Object Identifier: 10.2140/ant.2009.3.209

Subjects:
Primary: 11G30
Secondary: 11G35, 14C20, 14K20

Rights: Copyright © 2009 Mathematical Sciences Publishers

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Vol.3 • No. 2 • 2009
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