On Heegner Points for primes of additive reduction ramifying in the base field

Abstract

Let $E$ be a rational elliptic curve, and $K$ 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.