Local structure of the overconvergent de Rham-Witt complex

We give a general description of the structure of the relative de Rham-Witt complex on a polynomial ring, seen as an algebra over its integral part. After giving a control of the overconvergence of Lazard’s morphism, we similarly give the structure of the overconvergent complex, locally on a smooth algebraic variety over a perfect field of positive characteristic.