@inbook{10.2307/j.ctt130hk6f.5,
URL = {http://www.jstor.org/stable/j.ctt130hk6f.5},
abstract = {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 â S is a morphism of schemes, and if F and G are OX-modules, then a differential operator from F to G, relative to S, will be an fâ1(OS)-linear map h:F â G which is "almost" OX-linear. In order to make this precise, we begin by brutally linearizing h, i.e., by forming the obvious adjoint map:\[\overline{\text{h}}:{\text{O}_{{{\text{X}}^{\otimes }}_{{{\text{f}}^{-1}}({\text{O}_{\text{S}}})}}}\text{F}\to \text{G}\quad.\]Using the OX-module},
bookauthor = {Pierre Berthelot and Arthur Ogus},
booktitle = {Notes on Crystalline Cohomology. (MN-21)},
pages = {2.1--2.23},
publisher = {Princeton University Press},
title = {Calculus and Differential Operators.},
year = {1978}
}