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

Bianca Gouthier; Dajano Tossici

paper

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

arXiv:2403.09469

Abstract

If the characteristic of a field $k$ is odd any infinitesimal group scheme of $P G L_{2, k}$ lifts to $S L_{2, k}$ . 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 $P G L_{2, k}$ . Also, the infinitesimal trigonalizable case is considered.

9 pages