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Journal article

Application of covering techniques to families of curves

Abstract:

Much success in finding rational points on curves has been obtained by using Chabauty's Theorem, which applies when the genus of a curve is greater than the rank of the Mordell-Weil group of the Jacobian. When Chabauty's Theorem does not directly apply to a curve C, a recent modification has been to cover the rational points on C by those on a covering collection of curves Di, obtained by pullbacks along an isogeny to the Jacobian; one then hopes that Chabauty's Theorem applies to each Di. So...

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Journal:
Journal of Number Theory
Volume:
101
Issue:
2
Pages:
376-397
Publication date:
2003-08-01
DOI:
ISSN:
0022-314X
URN:
uuid:8cb4539c-6c9c-4e97-9afc-472764345207
Source identifiers:
25462
Local pid:
pubs:25462

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