nLab p-derivation

Idea

For a prime $p$, a $p$-derivation on a commutative ring $R$ is a map $\delta:R \to R$ such that $\phi(r) \coloneqq r^p + p \delta(r)$ is a ring homomorphism. $\phi$ is called the Frobenius lift attached to $\delta$.

An example of a $p$-derivation is the Fermat quotient.

Related pages

• arithmetic differential geometry
• Borger's absolute geometry
• derivation
• Joyal delta-ring