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Chabauty for symmetric powers of curves

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Siksek, Samir (2009) Chabauty for symmetric powers of curves. Algebra & Number Theory, Vol.3 (No.2). pp. 209-236. doi:10.2140/ant.2009.3.209

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Official URL: http://dx.doi.org/10.2140/ant.2009.3.209

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Abstract

Let C be a smooth projective absolutely irreducible curve of genus g >= 2 over a number field K, and denote its Jacobian by J. Let d >= 1 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 g - d . We give an explicit and practical criterion for showing that a given subset L subset of C-(d) (K) is in fact equal to C-(d) (K).

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Mathematics
Journal or Publication Title: Algebra & Number Theory
Publisher: Mathematical Sciences Publishers
ISSN: 1937-0652
Official Date: 2009
Dates:
DateEvent
2009Published
Volume: Vol.3
Number: No.2
Number of Pages: 28
Page Range: pp. 209-236
DOI: 10.2140/ant.2009.3.209
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Funder: Engineering and Physical Sciences Research Council (EPSRC), Marie Curie International

Data sourced from Thomson Reuters' Web of Knowledge

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