Unexpected subgroup schemes of PGL_{2,k} in characteristic 2

Bianca Gouthier; Dajano Tossici

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arXiv · 2403.09469

Unexpected subgroup schemes of PGL_{2,k} in characteristic 2

Bianca Gouthier·Dajano Tossici

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Abstract

If the characteristic of a field $k$ is odd any infinitesimal group scheme of $PGL_{2,k}$ lifts to $SL_{2,k}$. In this paper, we prove that this is not true in characteristic $2$ and we give a complete description, up to isomorphism, of infinitesimal unipotent subgroup schemes of $PGL_{2,k}$. Also, the infinitesimal trigonalizable case is considered.

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BibTeX RIS

Bianca Gouthier, Dajano Tossici. 2024-03-14. Unexpected subgroup schemes of PGL_{2,k} in characteristic 2. https://arxiv.org/abs/2403.09469

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