p-ADIC HEIGHT PAIRINGS AND INTEGRAL POINTS ON HYPERELLIPTIC CURVES

@inproceedings{Balakrishnan2013pADICHP,
  title={p-ADIC HEIGHT PAIRINGS AND INTEGRAL POINTS ON HYPERELLIPTIC CURVES},
  author={Jennifer S. Balakrishnan and A. Besser and J. Muller},
  year={2013}
}
  • Jennifer S. Balakrishnan, A. Besser, J. Muller
  • Published 2013
  • Mathematics
  • We give a formula for the component at p of the p-adic height pairing of a divisor of degree 0 on a hyperelliptic curve. We use this to give a Chabauty-like method for finding p-adic approximations to p-integral points on such curves when the Mordell-Weil rank of the Jacobian equals the genus. In this case we get an explicit bound for the number of such p-integral points, and we are able to use the method in explicit computation. An important aspect of the method is that it only requires a… CONTINUE READING
    11 Citations

    Tables from this paper.

    Explicit p-adic methods for elliptic and hyperelliptic curves
    • 5
    • PDF
    Quadratic Chabauty and rational points I: p-adic heights
    • 20
    • PDF
    Quadratic Chabauty and rational points II: Generalised height functions on Selmer varieties
    • 14
    • PDF
    An effective Chabauty-Kim theorem
    • 8
    • PDF
    Principal bundles and reciprocity laws in number theory
    • 2
    • PDF

    References

    SHOWING 1-10 OF 49 REFERENCES