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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
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: |
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| 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 |
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