We construct a t-structure on the stable infinity-category of cyclotomic spectra and show that the homotopy objects with respect to this t-structure on naturally Dieudonné modules, i.e., abelian groups equipped with operations V and F such that FV=p. For smooth schemes over perfect fields of characteristic p>0, these cyclotomic homotopy objects are the terms in the de Rham—Witt complex. As an application, I will explain how certain formal moduli problems associated to Calabi-Yau varieties admit cyclotomic interpretations, which can be used to strengthen past results about the behavior of these invariants under Fourier—Mukai equivalence.