Smoothness of stabilisers in generic characteristic

Benjamin Martin, David Stewart, Lewis Topley

Research output: Working paper

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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 languageEnglish
PublisherArXiv
Publication statusSubmitted - 30 Oct 2018

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Keywords

  • math.GR
  • math.AC
  • math.AG
  • math.RT

Cite this

Martin, B., Stewart, D., & Topley, L. (2018). Smoothness of stabilisers in generic characteristic. ArXiv.