Appears in collection : Conference on Arithmetic Geometry in honor of Luc Illusie

One of the obstacles in the definition of the singular support of a constructible sheaf in mixed characteristic is the absence of the cotangent bundle. We define a ‘Frobenius pull-back’ of the cotangent bundle restricted on the closed fiber of a flat regular scheme over a discrete valuation ring of mixed characteristic by using the sheaf of Frobenius-Witt differentials. We give some examples of constructible sheaves whose singular supports exist.