On quotients of affine superschemes over finite supergroups

Abstract

In this article we consider sheaf quotients of affine superschemes by finite supergroups that act on them freely. More precisely, if a finite supergroup $G$ acts on an affine superscheme $X$ freely, then the quotient $K$-sheaf $\tilde{X/G}$ is again an affine superscheme $Y$, where $K[Y]\simeq K[X]^G$. Besides, $K[X]$ is a finitely presented projective $K[X]^G$-module.