On complete reducibility in characteristic $p$

Abstract

Let $G$ be a reductive group over a field $k$ which is algebraically closed of characteristic $p \neq 0$. We prove a structure theorem for a class of subgroup schemes of $G$, for $p$ bounded below by the Coxeter number of $G$. As applications, we derive semi-simplicity results, generalizing earlier results of Serre proven in 1998, and also obtain an analogue of Luna's \'etale slice theorem for suitable bounds on $p$.

Locations

• Épijournal de Géométrie Algébrique - View - PDF
• arXiv (Cornell University) - View - PDF
• DOAJ (DOAJ: Directory of Open Access Journals) - View
• HAL (Le Centre pour la Communication Scientifique Directe) - View - PDF
• DataCite API - View