BALANCED DIAGONAL CLASSES AND RATIONAL POINTS ON ELLIPTIC CURVES

Let A be an elliptic curve over the rationals with multiplicative reduction at a prime p, and let K be a quadratic field in which p is inert. Under a generalized Heegner assumption, our previous contribution [5] to this volume attaches to (A, p, K) balanced diagonal classes in the Selmer groups of the p-adic Tate module of A over certain ring class fields of K. These classes are obtained as p-adic limits of geometric classes in the cohomology of higher-dimensional Kuga-Sato varieties. The main result of this paper relates these diagonal classes to p-adic logarithms of Heegner or Stark-Heegner points, depending on whether K is complex or real respectively.