## Balaji, V. and Deligne, P. and Parameswaran, A. J. - On complete reducibility in characteristic $p$

epiga:2201 - Épijournal de Géométrie Algébrique, September 1, 2017, Volume 1
On complete reducibility in characteristic $p$

Authors: Balaji, V. and Deligne, P. and Parameswaran, A. J.

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 étale slice theorem for suitable bounds on $p$.

Volume: Volume 1
Published on: September 1, 2017
Submitted on: June 27, 2017
Keywords: Mathematics - Algebraic Geometry,14L15, 14L24