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arXiv · 1607.08564

On complete reducibility in characteristic $p$

V. Balaji·P. Deligne·A. J. Parameswaran
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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 $p$.

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BibTeXRIS

V. Balaji, P. Deligne, A. J. Parameswaran. 2016-07-28. On complete reducibility in characteristic $p$. https://doi.org/10.46298/epiga.2017.volume1.2201

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