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2024-05-30

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cc-by (c) Gehrmann, Lennart et al., 2024
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/223126

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

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https://doi.org/10.1017/fms.2024.51

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.

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Espais de Hilbert, Teoria de Galois

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Hilbert space, Galois theory

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Articles publicats en revistes (Matemàtiques i Informàtica)

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GEHRMANN, Lennart and PATI, Maria Rosaria. L-invariants for cohomological representations of PGL(2) over arbitrary number fields. Forum of Mathematics. Sigma. Vol.  2024, num. 12. ISSN 2050-5094. [consulted: 12 of August of 2026]. Available at: https://hdl.handle.net/2445/223126

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