### Abstract

Original language | English |
---|---|

Publisher | ArXiv |

Publication status | Submitted - 30 Oct 2018 |

### Fingerprint

### Keywords

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

### Cite this

*Smoothness of stabilisers in generic characteristic*. ArXiv.

**Smoothness of stabilisers in generic characteristic.** / Martin, Benjamin; Stewart, David; Topley, Lewis.

Research output: Working paper

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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

PB - ArXiv

ER -