The aim of this corrigendum is to correct an error in Corollary 10.7 to Theorem 10.6, one of the main results in the paper ‘On the cuspidal cohomology of $S$-arithmetic subgroups of reductive groups over number fields’. This makes necessary a thorough investigation of the conditions under which a Cartan-type automorphism exists on $G_1=\mathrm {Res}_{\mathbb {C}/\mathbb {R}}G_0$, where $G_0$ is a connected semisimple algebraic group defined over $\mathbb {R}$.

中文翻译：

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更正：关于数域上还原性组的S-算术子组的尖峰同构

该勘误的目的是纠正推论10.7到定理10.6的错误，这是论文“关于$ S $-数量域上的归约组的算术子组的尖峰同同性”的主要结果之一。这使得必须对$ G_1 = \ mathrm {Res} _ {\ mathbb {C} / \ mathbb {R}} G_0 $上存在Cartan型自同构的条件进行彻底研究，其中$ G_0 $是连接的在$ \ mathbb {R} $上定义的半简单代数群。