Let $T$ be a torus over some field $k$ (not necessarily perfect). Is there a smallest extension $k'$ of $k$ such that $T \times_{\operatorname{Spec}k} \operatorname{Spec}k'$ is a split torus over $k'$? If so, how do you prove it?
2026-03-30 08:22:49.1774858969
Splitting field of a torus
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