μ p \mu _p - and α p \alpha _p -actions on K3 surfaces in characteristic p p

We consider μp\mu _p- and αp\alpha _p-actions on RDP K3 surfaces (K3 surfaces with rational double point (RDP) singularities allowed) in characteristic p>0p > 0. We study possible characteristics, quotient surfaces, and quotient singularities. It turns out that these properties of μp\mu _p- and αp\alpha _p-actions are analogous to those of Z/lZ\mathbb {Z}/l\mathbb {Z}-actions (for primes l≠pl \neq p) and Z/pZ\mathbb {Z}/p\mathbb {Z}-quotients respectively. We also show that conversely an RDP K3 surface with a certain configuration of singularities admits a μp\mu _p- or αp\alpha _p- or Z/pZ\mathbb {Z}/p\mathbb {Z}-covering by a “K3-like” surface, which is often an RDP K3 surface but not always, as in the case of the canonical coverings of Enriques surfaces in characteristic 22.