Congruences between Hilbert modular forms of weight $2$, and the Iwasawa $λ$-invariants

Yuichi Hirano

Published 2017-07-05Version 1

The purpose of this paper is to prove the equality between the algebraic Iwasawa $\lambda$-invariant and the analytic Iwasawa $\lambda$-invariant for a Hilbert cusp form of parallel weight $2$ at an ordinary prime $p$ when the associated residual Galois representation is reducible. This is a generalization of a result of R. Greenberg and V. Vatsal.