On heegner points for primes of additive reduction ramifying in the base field

Abstract

Let E be a rational elliptic curve and let K be an imaginary quadratic field. In this article we give a method to construct Heegner points when E has a prime bigger than 3 of additive reduction ramifying in the field K. The ideas apply to more general contexts, like constructing Darmon points attached to real quadratic fields, which is presented in the appendix.