Automorphic ℒ‐invariants for reductive groups
نویسندگان
چکیده
Let $G$ be a reductive group over number field $F$, which is split at finite place $\mathfrak{p}$ of and let $\pi$ cuspidal automorphic representation $G$, cohomological with respect to the trivial coefficient system Steinberg $\mathfrak{p}$. We use cohomology $\mathfrak{p}$-arithmetic subgroups attach $\mathcal{L}$-invariants $\pi$. This generalizes construction Darmon (respectively Spie\ss), who considered case $G=GL_2$ rationals totally real field). These depend priori on choice degree cohomology, in occurs. show that they are independent this provided $\pi$-isotypical part cyclic Venkatesh's derived Hecke algebra. Further, we can detected by completed cohomology. Combined local-global compatibility result Ding it follows for certain representations definite unitary groups equal Fontaine-Mazur associated Galois representation.
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ژورنال
عنوان ژورنال: Crelle's Journal
سال: 2021
ISSN: ['1435-5345', '0075-4102']
DOI: https://doi.org/10.1515/crelle-2021-0029