  We upgrade Howard's divisibility toward Perrin-Riou's Heegner point Main
Conjecture to an equality under some mild conditions. We do this by exploiting
Wei Zhang's proof of the Kolyvagin conjecture. The main ingredient is an
improvement of Howard's Kolyvagin system formalism. As another consequence of
it, we establish the equivalence between this main conjecture and the
primitivity of the Kolyvagin system in certain cases, by also exploiting a
explicit reciprocity law for Heegner points.
