Abstract

Given a Hida family $\cal{F}$ of tame level $W$, for a quadratic imaginary field $K$ that satisfies the Heegner hypothesis for $W$, one can construct some classes in the Galois cohomology of a self-dual twist of Hida's big Galois representation associated to $\cal{F}$, which are called big Heegner points. When two families intersect, a natural question is to compare the big Heegner points at the intersection. We show that the specializations at intersections agree up to multiplication by some Euler factor that arise from the difference in the tame levels.