  Beilinson Completion Algebras (BCAs) are generalizations of complete local
rings, and have a rich algebraic-analytic structure. These algebras were
introduced in my paper "Traces and Differential Operators over Beilinson
Completion Algebras", Compositio Math. 99 (1995). In the present paper BCAs are
used to give an explicit construction of the Grothendieck residue complex on an
algebraic scheme. This construction reveals new properties of the residue
complex, and in particular its interaction with differential operators.
Applications include: (i) results on the algebraic structure of rings of
differential operators; (ii) an analysis of the niveau spectral sequence of De
Rham homology; (iii) a proof of the contravariance of De Rham homology w.r.t.
etale morphisms; (iv) an algebraic description of the intersection cohomology
D-module of a curve.
