Let $G$ be a finite group and $A$ be a regular local ring on which $G$ acts. Under certain assumptions on $A$ and the action, Serre defined a function $a_{G}\colon G\rightarrow \mathbb{Z}$ which can be viewed as a higher dimensional analogue of Artin character, and conjectured that it is associated to a $\mathbb{Q}_{\ell }$ -rational representation of $G$ for any prime $\ell $ invertible in $A$ . We prove this conjecture in the equal characteristic case.
