Abstract:Let $E$ be a CM number field and $F$ its maximal real subfield. We prove a level-raising result for regular algebraic conjugate self-dual automorphic representations of $GL_{n}(\mathbb {A}_E)$. This generalizes previously known results of Thorne [Forum Math. Sigma 2 (2014)] by removing certain hypotheses occurring in that work. In particular, the level-raising prime $p$ is allowed to be unramified as opposed to inert in $F$, the field $E/F$ is not assumed to be everywhere unramified, and the field $E$ is allowed to be a general CM field.

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中文翻译：

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𝐺𝐿_{𝑛} 上自守形式的级别提升

摘要：设$E$为CM数域，$F$为最大实数子域。我们证明了 $GL_{n}(\mathbb {A}_E)$ 的正则代数共轭自对偶自守表示的水平提升结果。这概括了先前已知的 Thorne [Forum Math. Sigma 2 (2014)] 通过删除该工作中发生的某些假设。特别是，允许​​提升级别的素数 $p$ 是无分支的，而不是 $F$ 中的惰性，不假定字段 $E/F$ 处处无分支，并且允许字段 $E$一个通用的 CM 字段。

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