L-invariants for cohomological representations of PGL(2) over arbitrary number fields

Abstract

Let π be a cuspidal, cohomological automorphic representation of an inner form G of PGL2 over a number field F of arbitrary signature. Further, let p be a prime of F such that G is split at p and the local component πp of π at p is the Steinberg representation. Assuming that the representation is noncritical at p, we construct automorphic L-invariants for the representation π. If the number field F is totally real, we show that these automorphic L-invariants agree with the Fontaine–Mazur L-invariant of the associated p-adic Galois representation. This generalizes a recent result of Spieß respectively Rosso and the first named author from the case of parallel weight 2 to arbitrary cohomological weights.