Special cohomology classes for modular Galois representations

Building on ideas of Vatsal [Uniform distribution of Heegner points, Invent. Math. 148(1) (2002) 1–46], Cornut [Mazur's conjecture on higher Heegner points, Invent. Math. 148(3) (2002) 495–523] proved a conjecture of Mazur asserting the generic nonvanishing of Heegner points on an elliptic curve E/Q as one ascends the anticyclotomic Zp-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 two-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.