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- W3203898275 abstract "Let $pi$ be a cuspidal, cohomological automorphic representation of an inner form $G$ of $mathrm{PGL}_2$ over a number field $F$ of arbitrary signature. Further, let $mathfrak{p}$ be a prime of $F$ such that $G$ is split at $mathfrak{p}$ and the local component $pi_mathfrak{p}$ of $pi$ at $mathfrak{p}$ is the Steinberg representation. Assuming that the representation is non-critical at $mathfrak{p}$ we construct automorphic $mathcal{L}$-invariants for the representation $pi$. If the number field $F$ is totally real, we show that these automorphic $mathcal{L}$-invariants agree with the Fontaine-Mazur $mathcal{L}$-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." @default.
- W3203898275 created "2021-10-11" @default.
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- W3203898275 date "2021-09-30" @default.
- W3203898275 modified "2023-09-27" @default.
- W3203898275 title "L-invariants for cohomological representations of PGL(2) over arbitrary number fields" @default.
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