Constructs a hierarchy of regular curves with infinitesimal symmetries in all characteristics via infinitesimal group schemes from additive polynomials and numerical semigroup compactifications, plus non-abelian cohomology computations.
[Bri22b] , On models of algebraic group actions , Proc
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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.
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Generalizations of quasielliptic curves
Constructs a hierarchy of regular curves with infinitesimal symmetries in all characteristics via infinitesimal group schemes from additive polynomials and numerical semigroup compactifications, plus non-abelian cohomology computations.
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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.