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A flexible method for applying Chabauty's Theorem

Abstract:
A strategy is proposed for applying Chabauty's Theorem to hyperelliptic curves of genus > 1. In the genus 2 case, it shown how recent developments on the formal group of the Jacobian can be used to give a flexible and computationally viable method for applying this strategy. The details are described for a general curve of genus 2, and are then applied to find C(ℚ) for a selection of curves. A fringe benefit is a more explicit proof of a result of Coleman.
Publication status:
Published

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Publisher copy:
10.1023/A:1000111601294

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Journal:
COMPOSITIO MATHEMATICA
Volume:
105
Issue:
1
Pages:
79-94
Publication date:
1997-01-05
DOI:
ISSN:
0010-437X
URN:
uuid:009bd564-f789-4ef5-b90a-f98ae571a323
Source identifiers:
21499
Local pid:
pubs:21499

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