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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 D$_i$, obtained by pullbacks along an isogeny to the Jacobian; one then hopes that Chabauty's Theorem applies to each D$_...

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Publication date:
2003-01-01
URN:
uuid:bbcbf455-459c-408e-9662-fb8a07e8df89
Local pid:
oai:eprints.maths.ox.ac.uk:255

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