### Abstract

Let $R$ be a commutative unital ring. Given a finitely-presented affine $R$-group $G$ acting on a finitely-presented $R$-scheme $X$ of finite type, we show that there is a prime $p_0$ so that for any $R$-algebra $k$ which is a field of characteristic $p > p_0$, the centralisers in $G_k$ of all subsets $U \subseteq X(k)$ are smooth. We prove this using the Lefschetz principle together with careful application of Gr\"{o}bner basis techniques.

Original language | English |
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Publisher | ArXiv |

Publication status | Submitted - 30 Oct 2018 |

### Keywords

- math.GR
- math.AC
- math.AG
- math.RT

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## Cite this

Martin, B., Stewart, D., & Topley, L. (2018).

*Smoothness of stabilisers in generic characteristic*. ArXiv. http://arxiv.org/abs/1810.12628v1