Differential Modules of Complete Intersections

Abstract

The relevant facts about complete intersections are contained in appendix C. Here we shall study their differential modules. If R is a ring and M is an R-module, pd_R(M) will always denote the projective dimension of M. Suppose S/R is an algebra that is essentially of finite type. Choose a presentation

$$ S = R{[{X_1},...,{X_n}]_N}/I $$

with a multiplicatively closed set N of R[X₁,...,X_n].