  We prove that algebraic de Rham cohomology as a functor defined on smooth
$\mathbb{F}_p$-algebras is formally \'etale in a precise sense. To prove this,
we define and study the notion of a pointed $\mathbb{G}_a^{\text{perf}}$-module
and its refinement which we call a quasi-ideal in $\mathbb{G}_a^{\text{perf}}$
following Drinfeld. Our results show that given de Rham cohomology, one obtains
the theory of crystalline cohomology as its unique functorial deformation.
