Title: Residues and Differential Operators on Schemes
Publication status: appeared in Duke Math. J. 95 (1998), 305-341
Abstract:
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.
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(updated 2 June 2009)