The Stacks project

Situation 60.26.1. In Situation 60.7.5 assume the following

1. $S = \mathop{\mathrm{Spec}}(A)$ for some divided power ring $(A, I, \gamma )$ with $p \in I$,

2. there is given a homomorphism of divided power rings $\sigma : A \to A$ such that $\sigma (x) = x^ p \bmod pA$ for all $x \in A$.