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

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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.

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Forum of Mathematics, Sigma, 2024, vol. 12

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cc-by (c) Gehrmann, Lennart et al., 2024

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Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
L-invariants for cohomological representations of PGL(2) over arbitrary number fields