  We show that Illusie's derived de Rham cohomology (Hodge-completed) coincides
with Hartshorne's algebraic de Rham cohomology for a finite type map of
noetherian schemes in characteristic 0; the case of lci morphisms was a result
of Illusie. In particular, the E_1-differentials in the derived Hodge-to-de
Rham spectral sequence for singular varieties are often non-zero. Another
consequence is a completely elementary description of Hartshorne's algebraic de
Rham cohomology: it is computed by the completed Amitsur complex for any
variety in characteristic 0.
