  Derived de Rham cohomology has been recently used in several contexts, as in
works of Beilinson and Bhatt on p-adic periods morphisms and Morin on numerical
invariants for special values of zeta functions. Inspired by some results of
Morin, we aimed to compute Hodge completed derived de Rham complex in the case
of a rings map $\mathbb{Z}\longrightarrow k$, factoring through $\mathbb{F}_p$,
with $k$ a perfect ring (i.e. the Frobenius map is an automorphism).
