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Algebraic varieties with group operations given by morphisms, or group objects in the category of algebraic varieties, the category of algebraic schemes, or closely related categories.
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Commutator of algebraic subgroups is connected
This fact is Corollary 16.4.1 on page 40 of the course notes from (the first semester of) Brian Conrad's course on linear algebraic groups. In the notes there is a proof of this fact is modern languag …