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Solving Diophantine problems on curves via descent on the jacobian

Abstract:

We suggest that the following plan will provide a powerful tool for trying to find the set of Q-rational points C(Q) on a curve C of genus>1: (1) Attempt to find J(Q)/2J(Q) via descent on J, the Jacobian of C. (2) Deduce generators for J(Q) via an explicit theory of heights. (3). Apply local techniques to try to deduce C(Q) via an embedding of C(Q) inside J(Q). We describe work just completed, which gives versions of (1),(2),(3) which are often workable in practice for genus 2, and outline...

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E. V. Flynn More by this author
Publication date:
1995
URN:
uuid:e8541e5d-1571-401d-bb02-886f46a3e90b
Local pid:
oai:eprints.maths.ox.ac.uk:268

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