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We consider rational double point singularities (RDPs) that are non-taut,which means that the isomorphism class is not uniquely determined from the dualgraph of the minimal resolution. Such RDPs exist in characteristic $2,3,5$. Wecompute the actions of Frobenius, and other inseparable morphisms, on$W_n$-valued local cohomology groups of RDPs. Then we consider RDP K3 surfacesadmitting non-taut RDPs. We show that the height of the K3 surface, which isalso defined in terms of the Frobenius action on $W_n$-valued cohomologygroups, is related to the isomorphism class of the RDP.

Inseparable maps on $W_n$-valued local cohomology groups of non-taut rational double point singularities and the height of K3 surfaces