On the method of Coleman and Chabauty

@article{McCallum1994OnTM,
  title={On the method of Coleman and Chabauty},
  author={W. G. McCallum},
  journal={Mathematische Annalen},
  year={1994},
  volume={299},
  pages={565-596}
}
  • W. G. McCallum
  • Published 1994
  • Mathematics
  • Mathematische Annalen
  • Let C be a curve of genus g >_ 2, defined over a number field K , and let J be the Jacobian of C. Coleman [C2], following Chabauty, has shown how to obtain good bounds on the cardinality of C(K) if the rank r of the Mordell-Weil group J(K) is less than g. The key to the method is to construct a logarithm on J(Kv), for some valuation v of K , whose kernel contains J(K), and whose restriction to C(Kv) is represented explicitly as the integral of a differential. This paper is an attempt to make… CONTINUE READING
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