Number Theory Seminar
Thursday 22 February 2007, MR3, 4pm
Independence of Heegner Points (Joint work with Michael Rosen)
Joseph Silverman
(Brown)
Abstract:
Heegner points are special points on elliptic curves constructed from
CM points on a modular parametrization of the curve. There are many
known results about the dependence or independence of Heegner points
associated to a single quadratic imaginary field. In this talk I will
recall the construction of Heegner points and sketch a proof that
Heegner points corresponding to distinct CM fields are generally
linearly independent in the MordellWeil group. As time permits, I
will also discuss a negative implication for the elliptic curve
discrete logarithm problem via DeuringHeegner lifts and analogous
results for DarmonHeegner points attached to real quadratic
fields.



