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.

title = "Smoothness of stabilisers in generic characteristic",

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.",

keywords = "math.GR, math.AC, math.AG, math.RT",

author = "Benjamin Martin and David Stewart and Lewis Topley",

note = "15 pages",

year = "2018",

month = "10",

day = "30",

language = "English",

publisher = "ArXiv",

type = "WorkingPaper",

institution = "ArXiv",

}

TY - UNPB

T1 - Smoothness of stabilisers in generic characteristic

AU - Martin, Benjamin

AU - Stewart, David

AU - Topley, Lewis

N1 - 15 pages

PY - 2018/10/30

Y1 - 2018/10/30

N2 - 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.

AB - 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.

KW - math.GR

KW - math.AC

KW - math.AG

KW - math.RT

M3 - Working paper

BT - Smoothness of stabilisers in generic characteristic