Special cohomology classes for modular Galois representations

Building on ideas of Vatsal, Cornut proved a conjecture of Mazur asserting the generic nonvanishing of Heegner points on an elliptic curve E as one ascends the anticyclotomic Z_p-extension of a quadratic imaginary extension K/Q. In the present article Cornut's result is extended by replacing the elliptic curve E with the Galois cohomology of Deligne's 2-dimensional l-adic representation attached to a modular form of weight 2k>2, and replacing the family of Heegner points with an analogous family of special cohomology classes.