  We upgrade Howard's divisibility towards Perrin-Riou's Heegner point main
conjecture to the predicted equality. Contrary to previous works in this
direction, our main result allows for the classical Heegner hypothesis and
non-squarefree conductors. The main ingredients we exploit are W.~Zhang's proof
of Kolyvagin's conjecture, Kolyvagin's structure theorem for Shafarevich--Tate
groups, and the explicit reciprocity law for Heegner points.
