There is an error in the statement and proof of [VAV17, Proposition 5.1] that affects the statements of [VAV17, Corollaries 5.2 and 5.3]. In this note, we correct the statement of [VAV17, Proposition 5.1] and explain how to rectify subsequent statements. In brief, for a statement about abelian Galois representations of a fixed level, ‘abelian’ should be replaced with ‘liftable abelian’ (Definition 1). Statements about abelian Galois representations of arbitrarily high level, however, remain unchanged because such representations give rise to liftable abelian Galois representations of smaller, but still arbitrarily high, level. Hence the main theorems of the paper remain unchanged.

中文翻译：

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勘误：椭圆曲线的阿贝尔 n 分域和积库默尔和阿贝尔曲面的布劳尔群

[VAV17，命题 5.1] 的陈述和证明存在错误，影响了 [VAV17，推论 5.2 和 5.3] 的陈述。在本说明中，我们更正了 [VAV17, Proposition 5.1] 的陈述，并解释了如何更正后续陈述。简而言之，对于一个关于 a 的阿贝尔伽罗瓦表示的陈述固定的level, 'abelian' 应该替换为 'liftable abelian' （定义 1）。然而，关于任意高水平的阿贝尔伽罗瓦表示的陈述保持不变，因为这样的表示产生了较小但仍然任意高水平的可提升的阿贝尔伽罗瓦表示。因此，本文的主要定理保持不变。