We show that all of the nice behavior for Tamagawa numbers, Tate–Shafarevich sets, and other arithmetic invariants of pseudoreductive groups over global function fields, proved in another work, fails in general for noncommutative unipotent groups. We also give some positive results which show that Tamagawa numbers do exhibit some reasonable behavior for arbitrary connected linear algebraic groups over global function fields.

中文翻译：

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单能群算术不变量的病理行为

我们表明，在另一项工作中证明的 Tamagawa 数、Tate-Shafarevich 集和其他全局函数域上伪还原群的算术不变量的所有良好行为，对于非交换单能群通常都失败。我们还给出了一些积极的结果，这些结果表明，对于全局函数域上的任意连接的线性代数群，玉川数确实表现出一些合理的行为。