Hodge Completed Derived De Rham Algebra of a Perfect Ring

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 ℤ⟶ k, factoring through 𝔽_p, with k a perfect ring (i.e. the Frobenius map is an automorphism).