Let $U$ be a unipotent linear algebraic group over some field $k$ with char$k$=0. Let $U'$ be a linear algebraic group over $k$ such that $U'_{\bar{k}} = U_{\bar{k}}$ (ie $U'$ is a $\bar{k}/k$-twist of $U$).
Is $U'$ also unipotent?
2026-03-26 17:52:55.1774547575
twists of unipotent algebraic groups
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Yes.
Unipotence is (by definition) a "geometric" property.
Take a look at page 3/52 of
http://www.math.u-bordeaux1.fr/~jtong/Recherche/Unipotent.pdf