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Infinitesimal commutative unipotent group schemes with one-dimensional Lie algebra

2024/09/18 by Gouthier, Bianca
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.11997

Abstract

We prove that over an algebraically closed field of characteristic p>0 there are exactly, up to isomorphism, n infinitesimal commutative unipotent k-group schemes of order pn with one-dimensional Lie algebra, and we explicitly describe them. We consequently recover an explicit description of the pn-torsion of any supersingular elliptic curve over an algebraically closed field. Finally, we use these results to answer a question of Brion on rational actions of infinitesimal commutative unipotent group schemes on curves.

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