For infinitesimal commutative trigonalizable group schemes over perfect positive-characteristic fields, the Lie(G) dimension bound is the only obstruction to generically free rational actions on varieties.
Essential dimension of infinitesi mal commutative unipotent group schemes
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Infinitesimal rational actions
For infinitesimal commutative trigonalizable group schemes over perfect positive-characteristic fields, the Lie(G) dimension bound is the only obstruction to generically free rational actions on varieties.