In this chapter we develop Grothendieck's way of geometrizing the notions of calculus and differential geometry, and in particular the notion of a locally (or rather infinitesimally) constant sheaf. We begin by reviewing the formalism of differential operators.

If X → S is a morphism of schemes, and if F and G are O_{X}-modules, then a differential operator from F to G, relative to S, will be an f^{−1}(O_{S})-linear map h:F → G which is "almost" O_{X}-linear. In order to make this precise, we begin by brutally linearizing h, i.e., by forming the obvious adjoint map:

Using the O_{X}-module