On the Iwasawa invariants of BDP Selmer groups and BDP p-adic L-functions

Let p be an odd prime. Let f(1) and f(2) be weight 2 cuspidal Hecke eigenforms with isomorphic residual Galois representations at p. Greenberg-Vatsal and Emerton-Pollack-Weston showed that if p is a good ordinary prime for the two forms, the Iwasawa invariants of their p-primary Selmer groups and p-adic L-functions over the cyclotomic Z(p)-extension of Q are closely related. The goal of this article is to generalize these results to the anticyclotomic setting. More precisely, let K be an imaginary quadratic field where p splits. Suppose that the generalized Heegner hypothesis holds with respect to both (f(1), K) and (f(2), K). We study relations between the Iwasawa invariants of the BDP Selmer groups and the BDP p-adic L-functions of f(1) and f(2).