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

Abstract

Let p be an odd prime. Let f 1 {f_{1}} and f 2 {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 {\mathbb{Z}_{p}} -extension of ℚ {\mathbb{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 ) {(f_{1},K)} and ( f 2 , K ) {(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 {f_{1}} and f 2 {f_{2}} .