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

epiga:2201 - Épijournal de Géométrie Algébrique, September 1, 2017, Volume 1 - https://doi.org/10.46298/epiga.2017.volume1.2201
On complete reducibility in characteristic $p$

Authors: V. Balaji ; P. Deligne ; A. J. Parameswaran

    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
    Accepted on: June 27, 2017
    Submitted on: June 27, 2017
    Keywords: Mathematics - Algebraic Geometry,14L15, 14L24

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