Authors: V. Balaji ; P. Deligne ; A. J. Parameswaran
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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 $p$.
BĂśckle, Gebhard; Gajda, Wojciech; Petersen, Sebastian, 2019, On The Semisimplicity Of Reductions And Adelic Openness For đ¸-rational Compatible Systems Over Global Function Fields, Transactions Of The American Mathematical Society, 372, 8, pp. 5621-5691, 10.1090/tran/7788.