On $\mathcal{L}$-invariants associated to Hilbert modular forms

Abstract

Given a cuspidal Hilbert modular eigenform $\pi$ of parallel weight 2 and a nonarchimedian place $\mathfrak{p}$ of the underlying totally real field such that the local component of $\pi$ at $\mathfrak{p}$ is the Steinberg representation, one can associate two types of $\mathcal{L}$-invariants, one defined in terms of the cohomology of arithmetic groups and the other in terms of the Galois representation associated to $\pi$. We show that the $\mathcal{L}$-invariants are the same.

27 pages

References in corpus (1)

• Big principal series, p-adic families and L-invariants