Variation of anticyclotomic Iwasawa invariants in Hida families

Abstract

Building on the construction of big Heegner points in the quaternionic setting by Longo and Vigni, and their relation to special values of Rankin–Selberg $L$-functions established by Castella and Longo, we obtain anticyclotomic analogues of the results of Emerton, Pollack and Weston on the variation of Iwasawa invariants in Hida families. In particular, combined with the known cases of the anticyclotomic Iwasawa main conjecture in weight $2$, our results yield a proof of the main conjecture for $p$-ordinary newforms of higher weights and trivial nebentypus.