I'm studying automorphic forms and there's something I don't understand, when we talk about a connected reductive algebraic group $G$ defined over $\mathbb{Q}$, connected means connected as an algebraic group when we consider the corresponding complex algebraic group $G_\mathbb{C}$ obtained by extension of scalars?
2026-03-26 12:51:28.1774529488
About algebraic groups defined over Q
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Over $\mathbb{Q}$, connectedness usually means no nontrivial finite quotient.
See for example Milne's notes on Reductive Groups.