Geodesic
On the smoothness of normalisers, the subalgebra structure of modular Lie algebras, and the cohomology of small representations
Documenta mathematica, Tome 21 (2016), pp. 1-37.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We provide results on the smoothness of normalisers in connected reductive algebraic groups $G$ over fields $k$ of positive characteristic $p$. Specifically we we give bounds on $p$ which guarantee that normalisers of subalgebras of $\mathfrak{g}$ in $G$ are smooth, i.e.so that the Lie algebras of these normalisers coincide with the infinitesimal normalisers. One of our main tools is to exploit cohomology vanishing of small dimensional modules. Along the way, we obtain complete reducibility results for small dimensional modules in the spirit of similar results due to Jantzen, Guralnick, Serre and Bendel--Nakano--Pillen.
Classification : 17B45, 20G07, 20G10
Keywords: smoothness, subgroup structure, complete reducibility, cohomology 
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Herpel, Sebastian; Stewart, David I. On the smoothness of normalisers, the subalgebra structure of modular Lie algebras, and the cohomology of small representations. Documenta mathematica, Tome 21 (2016), pp. 1-37. http://geodesic.mathdoc.fr/item/DOCMA_2016__21__a43/