L-Invariant for Siegel--Hilbert Forms

We prove a formula for the Greenberg--Benois $\Ll$-invariant of the spin, standard and adjoint Galois representations associated with Siegel--Hilbert modular forms. In order to simplify the calculation, we give a new definition of the $\Ll$-invariant for a Galois representation $V$ of a number field $F\neq \Q$; we also check that it is compatible with Benois' definition for $Ind_F^\Q(V)$.

2010 Mathematics Subject Classification: 11R23, 11F80, 11F46, 11S25

Keywords and Phrases: Iwasawa Theory, L-invariants, p-adic L-functions, p-adic families of automorphic forms

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