Variation of anticyclotomic Iwasawa invariants in Hida families

TL;DR

This paper studies how anticyclotomic Iwasawa invariants vary within Hida families, extending previous results and proving the main conjecture for higher weight p-ordinary newforms with trivial nebentypus.

Contribution

It extends the variation results of Iwasawa invariants to higher weights and proves the main conjecture in new cases for p-ordinary forms.

Findings

Established anticyclotomic Iwasawa invariants variation in Hida families.

Proved the main conjecture for p-ordinary newforms of higher weights.

Connected big Heegner points with special L-values in the quaternionic setting.

Abstract

Building on the construction of big Heegner points in the quaternionic setting, and their relation to special values of Rankin-Selberg $L$-functions, we obtain anticyclotomic analogues of the results of Emerton-Pollack-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.