The rationality of Stark-Heegner points over genus fields of real quadratic fields

@inproceedings{Bertolini2005TheRO,
  title={The rationality of Stark-Heegner points over genus fields of real quadratic fields},
  author={Massimo Bertolini and Henri Darmon},
  year={2005}
}
We study the algebraicity of Stark-Heegner points on a modular elliptic curve E. These objects are p-adic points on E given by the values of certain p-adic integrals, but they are conjecturally defined over ring class fields of a real quadratic field K. The present article gives some evidence for this algebraicity conjecture by showing that linear combinations of Stark-Heegner points weighted by certain genus characters of K are defined over the predicted quadratic extensions of K. The non… CONTINUE READING

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