Geodesic
On complete reducibility in characteristic $p$
Épijournal de Géométrie Algébrique, Tome 1 (2017)

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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 $p$. 
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     title = {On complete reducibility in characteristic $p$},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
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}
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Balaji, V.; Deligne, P.; Parameswaran, A. J. On complete reducibility in characteristic $p$. Épijournal de Géométrie Algébrique, Tome 1 (2017). doi: 10.46298/epiga.2017.volume1.2201

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