| Résume | We consider a finite group $G$ acting on a polynomial ring in $n$ variables over a field. We are interested in the ring of invariants and would like to know a bound on the degrees of the elements of a set of generators. In characteristic $0$ such a bound is the order of the group $|G|$, but in the modular case any bound must also involve $n$. We will show how to prove that the Castelnuovo-Mumford regularity of the ring of invariants is at most $0$ and thus, as a corollary, confirm a conjecture of Kemper that $n(|G|-1)$ is a bound. |
