Stark-Heegner points over real quadratic fields, by Henri R. Darmon

This paper has appeared in Number theory (Tiruchiropalli, 1996), 41-69, Contemp. Math. 210, Amer. Math. Soc., Providence, RI, 1998 and so the dvi version has been removed. Let E be a modular elliptic curve over Q of prime conductor p. This paper describes a conjectural p-adic analytic construction of a global point on E over K, where K is a real quadratic field satisfying suitable conditions. This global point is constructed via modular symbols, i.e., special values of L-functions. The conjecture is tested numerically on certain elliptic curves of conductor 11 and 37.

The conjecture of this paper was suggested by an earlier result of M. Bertolini and the author, where the field K was imaginary quadratic. In this case the predicted formula was proved, thanks to the theory of complex multiplication and the Cerednik-Drinfeld theory of p-adic uniformization of Shimura curves.



Henri R. Darmon < darmon@math.mcgill.ca>